Calculus A Complete Course Canadian 8th Edition Adams - Test Bank

Calculus A Complete Course Canadian 8th Edition Adams – Test Bank

 

Instant Download – Complete Test Bank With Answers

 

 

Sample Questions Are Posted Below

 

Chapter 5  Integration

 

5.1  Sums and Sigma Notation

 

1) Write sigma notation of 4 – 9 + 16 – 25 +… + .

1. A) (k + 1)2
2. B) k2
3. C) k2
4. D) (k + 1)2
5. E) (k – 1)2

Answer:  B

Diff: 1

 

2) Evaluate the sum .

1. A) 420
2. B) 70
3. C) 67
4. D) 417
5. E) 356

Answer:  A

Diff: 1

 

 

3) Evaluate .

1. A) 1 +

B)

1. C) –
2. D) 1 –
3. E) –

Answer:  C

Diff: 1

4) Evaluate the .

1. A) +
2. B) –

C)

1. D) 2 –
2. E) 2 +

Answer:  A

Diff: 1

 

5) Find and evaluate the sum .

A)

1. B) –

C)

1. D) –

E)

Answer:  B

Diff: 2

 

6) Evaluate .

1. A) -1
2. B) 0
3. C) 51
4. D) 1
5. E) 101

Answer:  D

Diff: 2

7) Express the sum   +  +  +  +…..  +    using sigma notation.

A)

B)

C)

D)

E)

Answer:  A

Diff: 2

 

8) Simplify the expression .

1. A) ln((2n)!)

B)

1. C) (2 ln n)!
2. D) 2 ln(n!)
3. E) (ln(n))!

Answer:  D

Diff: 2

 

 

9) Express the sum in the series .

1. A) 2k3+ 9k2+ 7k
2. B) 2k3+ 9k2+ 5k
3. C) 3k3+ 9k2+ 7k
4. D) 3k3+ 9k2+ 5k
5. E) 2k3- 9k2+ 7k

Answer:  A

Diff: 3

10) Evaluate the sum   Hint:   =  – .

1. A) 1

B)

C)

D)

E)

Answer:  C

Diff: 3

 

11) Evaluate the sum  .

A)

B)

C)

D)

E)

Answer:  D

Diff: 3

 

 

12) Express the sum  as a polynomial function of n.

1. A) 3n3+  n2 +  n
2. B) 3n3+ n2 –  n
3. C) 3n3+ n2 + 4n
4. D) 3n3 + 3 n2- n
5. E) 3n3- n2 –  n

Answer:  E

Diff: 1

5.2  Areas as Limits of Sums

 

1) Find an approximation for the area under the curve  y = 1 –   and above the x-axis from  x =  0  to

x = 1  using a sum of areas of four  rectangles each having width  1/4  and  (a) tops lying under the curve,  or  (b) tops lying above the curve.  What does this tell you about the actual area under the curve?

1. A) (a) , (b)   ;     <  area under curve  <
2. B) (a) , (b)   ;     <  area under curve  <
3. C) (a) , (b)   ;     <  area under curve  <
4. D) (a) , (b)   ;     <  area under curve  <
5. E) (a) , (b)   ;     <  area under curve  <

Answer:  A

Diff: 1

 

 

2) Given that the area under the curve  y = x2  and above the x-axis from  x = 0  to  x = a > 0  is   square units, find the area under the same curve from  x = -2  to  x = 3.

1. A) square units
2. B) square units
3. C) 9 square units
4. D) 6 square units

E)

Answer:  A

Diff: 2

3) Construct  and simplify a sum approximating the area above the x-axis and under the curve  y = x2  between x = 0  and  x = 3  by using  n  rectangles having equal widths  and tops lying under or on the curve.  Find the actual area as a suitable limit.

1. A) , area = 9 square units
2. B) , area = 9 square units
3. C) , area = 6 square units
4. D) , area = 6 square units
5. E) , area = 9 square units

Answer:  A

Diff: 1

 

4) Construct and simplify a sum approximating the area above the x-axis and under the curve  y = x2  between x = 0  and  x = 3  by using  n  rectangles having equal widths  and tops lying above or on the curve.  Find the actual area as a suitable limit.

1. A) , area = 9 square units
2. B) , area = 9 square units
3. C) , area = 6 square units
4. D) , area = 6 square units
5. E) , area = 9 square units

Answer:  A

Diff: 1

5) Write the area under the curve  y = cos x  and above the interval  [0, π/2]  on the x-axis as the limit of a sum of areas of  n  rectangles of equal widths.  Have the upper-right corners of the rectangles lie on the curve.

1. A) Area =
2. B) Area =
3. C) Area =
4. D) Area =
5. E) Area =

Answer:  A

Diff: 2

 

6) Given that =  ,  find the area under  y = x3  and above the interval  [0, a]  on the x-axis  (where  a > 0 )  by interpreting the area as a limit of a suitable sum.

1. A) square units
2. B) square units
3. C) square units
4. D) square units
5. E) square units

Answer:  A

Diff: 2

 

7) The limit   represents the area of a certain region in the xy-plane. Describe the region.

1. A) region under y = cos x, above  y = 0,  between x = 0  and  x =
2. B) region under y = sin x, above  y = 0,  between x = 0  and  x =
3. C) region under y = cos x, above  y = 0,  between x = 0  and  x = π
4. D) region under y = sin x, above  y = 0,  between x = 0  and  x = π
5. E) region under y = cos x, above  y = 0,  between x=  and  x = π

Answer:  D

Diff: 2

 

8) By interpreting it as the area of a region in the xy-plane, evaluate the limit

 

.

1. A) 2 + 2π (the area of the trapezoidal region under y = 1 + πx,  above  y = 0  from  x = 0  to  x = 2)
2. B) 1 + π (the area of the trapezoidal region under y = 1 + 2πx,  above  y = 0  from  x = 0  to  x = 1)
3. C) 2 + 4π (the area of the trapezoidal region under y = 1 + 2πx,  above  y = 0  from  x = 0  to  x = 2)
4. D) 4 + 2π (the area of the trapezoidal region under y = 2 + πx,  above  y = 0  from  x = 0  to  x = 2)
5. E) 2 + (the area of the trapezoidal region under  y = 2 + πx,  above  y = 0  from  x = 0  to  x = 1)

Answer:  A

Diff: 2

 

9) By interpreting it as the area of a region in the xy-plane, evaluate the limit

 

.

1. A) π (the area of a quarter of a circular disk of radius 2)
2. B) 2π (the area of half of a circular disk of radius 2)
3. C) 4π (the area of a circular disk of radius 2)
4. D) 8π (the area of half of a circular disk of radius 4)
5. E) 16π (the area of a circular disk of radius 4)

Answer:  A

Diff: 2

 

5.3  The Definite Integral

 

1) Let  P denote the partition of the interval  [1, 3]  into 4 subintervals of equal length Δx = 1/2.

Evaluate the upper and lower Riemann sums  U(f, P)  and  L(f,P) for the function  f(x) = 4 x2.

1. A) U(f,P) = 40, L(f,P) = 30
2. B) U(f,P) = 41, L(f,P) = 29
3. C) U(f,P) = 42, L(f,P) = 28
4. D) U(f,P) = 43, L(f,P) = 27
5. E) U(f,P) = 44, L(f,P) = 26

Answer:  D

Diff: 1

 

2) Let  P denote the partition of the interval  [1, 2]  into 8 subintervals of equal length Δx = 1/8.

Evaluate the upper and lower Riemann sums  U(f, P)  and  L(f,P) for the function  f(x) = 1/x.

Round your answers to 4 decimal places.

1. A) U(f,P) = 0.7110, L(f,P) = 0.6781
2. B) U(f,P) = 0.7254, L(f,P) = 0.6629
3. C) U(f,P) = 0.7302, L(f,P) = 0.6571
4. D) U(f,P) = 0.7378, L(f,P) = 0.6510
5. E) U(f,P) = 0.7219, L(f,P) = 0.6683

Answer:  B

Diff: 1

 

3) Let  P denote the partition of the interval  [1, 4]  into 6 subintervals of equal length Δx = 1/2.

Evaluate the upper and lower Riemann sums  U(f, P)  and  L(f,P) for the function  f(x) = .

Round your answers to 4 decimal places.

4. A) U(f,P) = 4.9115, L(f,P) = 4.4115
5. B) U(f,P) = 4.9135, L(f,P) = 4.4109
6. C) U(f,P) = 4.9180, L(f,P) = 4.4057
7. D) U(f,P) = 4.9002, L(f,P) = 4.4250
8. E) U(f,P) = 4.9183, L(f,P) = 4.4093

Answer:  A

Diff: 1

 

 

4) Calculate the upper Riemann sum for  f(x) = x2 + 1  corresponding to a partition  P  of the interval  [0, 3]  into n equal subintervals of length 3/n.  Express the sum in closed form and use it to calculate the area under the graph of  f,  above the x-axis,  from  x = 0  to  x = 3.

1. A) U(f,P) = + 3, area = 12 square units
2. B) U(f,P) = + 3, area = 12 square units
3. C) U(f,P) = + 3, area = 12 square units
4. D) U(f,P) = + 3, area = 12 square units
5. E) U(f,P) = + 3, area = 12 square units

Answer:  C

Diff: 1

5) Calculate the lower Riemann sum for  f(x) = ex corresponding to a partition  P  of the interval  [0, 1]  into n equal subintervals of length  1/n.  Given that n  = 1  (which can be verified by using l’Hopital’s Rule),  find the area under y = ex and above the x-axis between  x = 0  and  x = 1.

1. A) L(f,P) = , area = e square units
2. B) L(f,P) = , area = square units
3. C) L(f,P) = , area = e – 1 square units
4. D) L(f,P) = , area = square units
5. E) L(f,P) = , area = square units

Answer:  C

Diff: 2

 

 

6) Express  dx  as a limit of Riemann sums corresponding to partitions of  [0, 1]  into equal subintervals and using the values of  f  at the midpoints of the subintervals.

1. A) dx =
2. B) dx =
3. C) dx =
4. D) dx =
5. E) dx =

Answer:  E

Diff: 2

7) Express  dx  as a limit of lower Riemann sums corresponding to partitions of  [0, 2]  into equal subintervals.

1. A) dx = .
2. B) dx = .
3. C) dx =  .
4. D) dx = .
5. E) dx = .

Answer:  A

Diff: 2

 

 

8) Write the following limit as a definite integral:

.

1. A)

B)

C)

D)

E)

Answer:  A

Diff: 2

9) Write the following limit as a definite integral:

 

1. A)

B)

C)

D)

E)

Answer:  A

Diff: 2

 

 

10) Use the limit definition of definite integral to evaluate dx.

1. A) 0
2. B) –

C)

1. D) 1
2. E) -1

Answer:  A

Diff: 2

 

11) Use the limit definition of the definite integral to evaluate dx.

1. A) 10
2. B) 18
3. C) 6
4. D) 30
5. E) 9

Answer:  D

Diff: 2

12) Write the following limit as a definite integral:

1. A) dx
2. B) dx
3. C) dx
4. D) dx
5. E) dx

Answer:  A

Diff: 3

 

 

5.4  Properties of the Definite Integral

 

1) Given that  and  = -1,  find

1. A) -3
2. B) -1
3. C) 3
4. D) 1
5. E) -2

Answer:  A

Diff: 1

 

2) Suppose that

1. A) -5
2. B) -3
3. C) -7
4. D) -1
5. E) 7

Answer:  C

Diff: 2

3) Evaluate dx.

1. A) 42
2. B) 0
3. C) 21
4. D) 51
5. E) 16

Answer:  A

Diff: 1

 

4) True or False:   If f and g are integrable functions on the interval [a, b], then

= . dx.

Answer:  FALSE

Diff: 1

 

 

5) Evaluate  dx.

1. A) 0
2. B) 1
3. C) -1

D)

1. E) –

Answer:  B

Diff: 2

 

6) True or False:  If  f(x) is an even function and g(x) is an odd function over the same interval [-a, a], then

 

Answer:  TRUE

Diff: 1

7) Evaluate (2 – ) dx  by interpreting the integral as representing an area.

A)

1. B) 4
2. C) 2

D)

1. E) –

Answer:  A

Diff: 1

 

8) Evaluate  dx  by interpreting the integral as representing an area.

1. A) 8π
2. B) 4π
3. C) 16π
4. D) 8
5. E) 16

Answer:  A

Diff: 1

 

 

9) Given that   dx = ,  evaluate   dx.

1. A) π/4
2. B) π/2
3. C) π
4. D) 1/2

E)

Answer:  A

Diff: 1

 

10) Given the piecewise continuous function  f(x) =

evaluate  by using the properties of definite integrals and interpreting integrals as areas.

Answer:   8

Diff: 2

11) Find the average value of the function  f(x) = 3 + 4x  on  [0, 2].

1. A) 7
2. B) 6
3. C) 8
4. D) 3
5. E) 9

Answer:  A

Diff: 1

 

12) Find the average value of the function  f(x) = sin (x/2) + π  on  [-π, π].

1. A) π

B)

1. C) 2π

D)

1. E) 2

Answer:  A

Diff: 1

 

 

13) What is the average value of  f(x) =   on the interval  [0, 2]?

A)

B)

1. C) π

D)

1. E) 2π

Answer:  A

Diff: 1

 

14) What values of a and b, satisfying  a < b,  maximize the value of

1. A) a = 0, b = 1
2. B) a = -1, b = 1
3. C) a = 0, b = 2
4. D) a = -∞, b = ∞
5. E) a = -1, b = 0

Answer:  A

Diff: 3

15)  What values of a and b, satisfying  a < b,  maximize the value of

1. A) a = -2, b = 4
2. B) a = 0, b = 4
3. C) a = -∞, b = ∞
4. D) a = -2, b = 0
5. E) a = 1, b = 3

Answer:  A

Diff: 3

 

 

5.5  The Fundamental Theorem of Calculus

 

1) Evaluate the definite integral

1. A) –

B)

C)

1. D) –
2. E) -12

Answer:  B

Diff: 1

 

2) Compute the definite integral – 2x + 1)dx.

1. A) 14
2. B) 22
3. C) 21
4. D) 24
5. E) 20

Answer:  D

Diff: 1

3) Compute the integral – x)dx.

1. A) 4-
2. B) 4+
3. C) 4-
4. D) 4 +
5. E) 2 –

Answer:  A

Diff: 2

 

 

4) Compute the integral

A)

B)

1. C) –
2. D) –

E)

Answer:  B

Diff: 2

 

5) Evaluate the integral dx.

A)

1. B) 1

C)

D)

E)

Answer:  A

Diff: 2

6) Find dx.

1. A)

B)

C)

D)

E)

Answer:  D

Diff: 2

 

7) Evaluate the integral

A)

B)

C)

D)

1. E) –

Answer:  C

Diff: 2

 

8) Find the average value of the function f(x) = x4 + 3×3 – 2×2 – 3x + 1 on the interval [0, 2].

A)

B)

C)

D)

E)

Answer:  A

Diff: 2

9) Find the average value of the function f(x) = sin x on [0, 3π/2].

A)

B)

C)

D)

E)

Answer:  B

Diff: 2

 

 

10) Evaluate the definite integral dx.

11. A) 11.1
12. B) 9.9
13. C) 10.1
14. D) 15
15. E) -10.1

Answer:  C

Diff: 2

 

11) Evaluate the integral dx.

1. A) 4
2. B) 6
3. C) 7
4. D) 5
5. E) 3

Answer:  D

Diff: 2

 

12) Evaluate the integral

1. A) 1
2. B) 0
3. C) -1
4. D) -2
5. E) 2

Answer:  A

Diff: 1

13) Find the average value of the function f(x) = sec2 3x,over the interval [-π/12, π/12].

A)

B)

C)

D)

E)

Answer:  C

Diff: 2

 

14) Let  f(t) =

Evaluate  dt.

Answer:

dt.=

Diff: 3

 

15) Evaluate the definite integral dx.

1. A) –

B)

C)

1. D) -33

E)

Answer:  C

Diff: 2

16) Find the derivative of  F(x) =

1. A) 2 ln x
2. B) 0
3. C) -ln xn x
4. D) ln x
5. E) ln x

Answer:  D

Diff: 2

 

 

17) Find the derivative of F(x) = dt.

1. A) 2e2xcos (e4x)
2. B) 2e2xsin (e4x)
3. C) 2e2xcos (e2x)
4. D) e2xcos (e4x)
5. E) excos (e4x)

Answer:  A

Diff: 2

 

18) Given that the relation  3×2 + dt = 3  defines y implicitly as a differentiable function of x, find .

A)

B)

1. C) 6x + cos (t) – t sin (t)
2. D) 6x +cos(y) – ysin (y)
3. E) 6x + ycos (y)

Answer:  A

Diff: 3

19) Evaluate

1. A) –
2. B) –

C)

1. D) 1
2. E)

Answer:  B

Diff: 3

 

 

20) Find the point on the graph of the function  f(x) = dt  where the graph has a horizontal tangent line.

A)

B)

C)

1. D) (1, 0)

E)

Answer:  A

Diff: 3

 

21) True or False: Since the derivative of –  is , the Fundamental Theorem of Calculus implies that

dx = –  +  = -2.

Answer:  FALSE

Diff: 3

5.6  The Method of Substitution

 

1) Evaluate the integral  dx.

1. A) (6 + x)16 +  C
2. B) (6 + x)15 +  C
3. C) (6 + x)16 +  C
4. D) – (6 + x)16 +  C
5. E) – (6 + x)16 +  C

Answer:  A

Diff: 1

 

 

2) Find the inflection point of the function f(x) = dt, where x > 0.

1. A) (1, 0)
2. B) (e, )
3. C) (e, 1)
4. D) (e, )

E)

Answer:  D

Diff: 3

 

3) Evaluate the integral dx.

1. A) ln(3) + C
2. B) ln + C
3. C) 3ln + C
4. D) + C
5. E) + C

Answer:  C

Diff: 1

4) Evaluate the integral  dx.

1. A) e(x2 + 2x + 3)+ C
2. B) e(x2 + 2x + 3)+ C
3. C) – e (x2 + 2x + 3)+ C
4. D) – e(x2 + 2x + 1)+ C
5. E) 2 e(x2 + 2x + 3)+ C

Answer:  A

Diff: 1

 

 

5) Evaluate the integral

1. A) –
2. B) +
3. C) –
4. D) +

E)

Answer:  D

Diff: 2

 

6) Evaluate the integral  dx.

1. A) + C
2. B) + C
3. C) + C
4. D) + C
5. E) + C

Answer:  C

Diff: 2

7) Evaluate the integral dx.

1. A) ln(x2+ 4x + 5) + C
2. B) 2 ln(x2+ 4x + 5) + C
3. C) ln(x2+ 4x + 5) + C
4. D) -2 ln(x2+ 4x + 5) + C
5. E) – ln(x2+ 4x + 5) + C

Answer:  C

Diff: 2

 

 

8) Evaluate the integral dx.

1. A) + C
2. B) + C
3. C) + C
4. D) + C
5. E) + C

Answer:  B

Diff: 2

 

9) Evaluate the integral  dx.

1. A) + C
2. B) + C
3. C) + C
4. D) + C
5. E) + C

Answer:  D

Diff: 2

10) Evaluate the integral dx.

1. A) + C
2. B) -3 + C
3. C) + C
4. D) – + C
5. E) – + C

Answer:  A

Diff: 2

 

 

11) Evaluate the integral cos (e2x) dx.

1. A) + C
2. B) + C
3. C) – + C
4. D) – + C
5. E) + C

Answer:  B

Diff: 2

 

12) Evaluate dx.

1. A) 1
2. B) 0
3. C) 2

D)

1. E) π

Answer:  A

Diff: 2

13) Evaluate (3x) (3x) dx.

1. A) sin(3x) + C
2. B) sin(3x) + C
3. C) sin(3x) + C
4. D) sin(3x) + C
5. E) sin(3x) + C

Answer:  A

Diff: 2

 

 

14) Evaluate (πx) dx.

A)

B)

1. C) 1

D)

1. E) π

Answer:  A

Diff: 2

 

15) Evaluate x  x dx.

A)

B)

C)

D)

1. E) π

Answer:  A

Diff: 2

16) Evaluate x dx.

1. A) –
2. B) +

C)

D)

1. E) –

Answer:  A

Diff: 2

 

 

17) Evaluate .

1. A)
2. B)
3. C) π
4. D) 1

E)

Answer:  A

Diff: 2

 

18) Evaluate sinh(x) dx

1. A) 2 excosh(x) + C
2. B) – + C
3. C) e2x- x + C
4. D) 2 excosh(x) – 2exsinh(x) + C
5. E) e2x+ x + C

Answer:  C

Diff: 2

19) Evaluate the integral

1. A) +  + C
2. B) +  + C
3. C) +  + C
4. D) +  + C
5. E) –  + C

Answer:  D

Diff: 2

 

 

20) Evaluate the integral dx.

1. A) + C
2. B) – + C
3. C) + C
4. D) – + C
5. E) + C

Answer:  D

Diff: 3

 

21) Evaluate the integral dx.

1. A) – + C
2. B)  + C
3. C) – + C
4. D)  + C
5. E) – + C

Answer:  A

Diff: 2

22) Evaluate the integral dx.

1. A) + C
2. B) + C
3. C) ln+ C
4. D) ln+ C
5. E) ln+ C

Answer:  D

Diff: 2

 

23) Evaluate the integral dx.

1. A) tan-1+ C
2. B) tan-1+ C
3. C) tan-1+ C
4. D) tan-1+ C
5. E) tan-1+ C

Answer:  C

Diff: 2

 

24) Evaluate  dx.

1. A) 2ln+ C
2. B) + ln+ C
3. C) ln+ C

D)

1. E) + C

Answer:  C

Diff: 2

25) True or False:  dx = –  + C

Answer:  TRUE

Diff: 2

 

26) Evaluate the integral dx.

1. A) + C
2. B) + C
3. C) + C
4. D) + C
5. E) 2+ C

Answer:  A

Diff: 3

 

27) Evaluate the integral dx.

1. A) – + C
2. B) – + C
3. C) – + C
4. D) + + C
5. E) – + C

Answer:  B

Diff: 3

 

28) Evaluate the integral dx.

1. A) tan-1(et) + C
2. B) tan-1(e2t) + C
3. C) tan-1(et) + C
4. D) tan-1(e2t) + C
5. E) tan-1(e4t) + C

Answer:  B

Diff: 3

29) Evaluate the integral dx.

1. A) + C
2. B) + C
3. C) + C
4. D) + C
5. E) 2+ C

Answer:  D

Diff: 3

 

 

5.7  Areas of Plane Regions

 

1) Find the area of the finite plane  region bounded by the graphs of the equations y = x4 and y = 4.

1. A) square units
2. B) square units
3. C) square units
4. D) square units
5. E) 1 square unit

Answer:  B

Diff: 1

 

2) Find the area of the finite plane region bounded by the graphs of the equations y = x3, y = 0, x = 1, and
x = 3.

1. A) 10 square units
2. B) 15 square units
3. C) 20 square units
4. D) 25 square units
5. E) 30 square units

Answer:  C

Diff: 1

3) Find the area of the finite plane region bounded by the graphs of the equations y = ,  ,
x = 4.

1. A) square units
2. B) square units
3. C) square units
4. D) 11 square units
5. E) square units

Answer:  C

Diff: 1

 

 

4) Find the area of the finite region bounded by the graphs of the equations y = x2 – 4  and  y = 4 – x2.

1. A) 16 square units
2. B) 22 square units
3. C) square units
4. D) square units
5. E) square units

Answer:  D

Diff: 2

 

5) Find the area of the region lying in the first quadrant above the curve  xy = 4 and below the line
x + y = 5.

Answer:   – 8 ln(2) square units

Diff: 2

 

6) Find the area of the region lying in the first quadrant above the curve  xy = 4 and below the line
x + y = 5.

1. A) + 4 ln(5) square units
2. B) – 8 ln(2) square units
3. C) – 8 ln(2) square units
4. D) + 8 ln(2) square units
5. E) – 4 ln(5) square units

Answer:  B

Diff: 2

7) Find the area of the finite plane region bounded by the graphs of the equations y = x5,  x = 0, and
y = 81.

1. A) square units
2. B) 334 square units
3. C) square units
4. D) 203 square units
5. E) square units

Answer:  E

Diff: 2

 

 

8) Find the area of the finite region bounded by the graphs of the functions  f(x) = x2 and  g(x) = x3.

1. A) square units
2. B) square units
3. C) square units
4. D) square units
5. E) square units

Answer:  E

Diff: 1

 

9) Find the area of the region enclosed by the graphs of  y = ex  and  y = 1 – 2x  from x = 0 to x = 1.

1. A) e – 1 square units
2. B) e + 1 square units
3. C) e square units
4. D) 1 – e square units
5. E) 1 square unit

Answer:  A

Diff: 1

10) Find the area of the region enclosed by the curves y = cosh(x), y = – sinh(x), and 0 ≤ x ≤ ln(4) (shown in the figure below).

 

Answer:  area = 3 square units

Diff: 2

 

 

11) Find the area of the region bounded by the graphs of the equations x = y2 – 2 and y = -x.

1. A) square units
2. B) square units
3. C) 3 square units
4. D) square units
5. E) square units

Answer:  D

Diff: 2

 

12) Find the area of the finite region in the first quadrant bounded by the graphs of the equations 3y2 = x3  and  y2 = 3x.

1. A) square units
2. B) square units
3. C) square units
4. D) square units
5. E) square units

Answer:  C

Diff: 2

13) Find the area of the finite plane region bounded by the graphs of the equations y = cot x, y = 0, , and .

1. A) ln 2 square units
2. B) ln 2 square units
3. C) ln 2 square units
4. D) ln 2 square units
5. E) 2 ln 2 square units

Answer:  B

Diff: 2

 

 

14) Find the area of the first quadrant region lying under the curve  +   = , where a > 0.

1. A) square units
2. B) square units
3. C) square units
4. D) square units
5. E) square units

Answer:  D

Diff: 2

 

15) Find the area of the region lying between the graphs of the equations y = sin x and y = cos x from 0 to 2π.

1. A) 2 square units
2. B) 4 square units
3. C) 6 square units
4. D) 3 square units
5. E) square units

Answer:  B

Diff: 3

16) Find the area inside the circle x2 + y2 = a2 and outside the ellipse b2 x2 + a2 y2 = a2 b2,  here a > b.

1. A) πa square units
2. B) square units
3. C) 2πa square units
4. D) square units
5. E) πb(a – b) square units

Answer:  A

Diff: 3

 

 

17) Find the constant real number m such that the line y = mx bisects the area of the finite plane region enclosed by the curve y = 2x – x2 and the x-axis. Refer to the figure below.

 

Answer:  m = 2 – ≈ 0.413

Diff: 2

 

18) Find the area of the region bounded by the graphs of the equations y2 = 2px  and x2 = 2py ,
where p > 0.

1. A) p3square units
2. B) p2square units
3. C) p2square units
4. D) p2square units
5. E) 2p2square units

Answer:  C

Diff: 3

19) Find the total area of the two finite plane regions bounded by the curves x2 + y = 4  and  x2 y = 3.

1. A) 8- square units
2. B) 8- square units
3. C) 8- square units
4. D) 8- square units
5. E) 8- 14 square units

Answer:  C

Diff: 3