Free Printable Unit 6 AB Test Review

1.

What does this picture represent?

a)

Left Riemann Sum

b)

Right Riemann Sum

c)

Middle Riemann Sum

d)

Trapezoidal Sum

2.

What does this picture represent?

a)

Left Riemann Sum

b)

Right Riemann Sum

c)

Middle Riemann Sum

d)

Trapezoidal Sum

3.

What does picture represent?

a)

Left Riemann Sum

b)

Right Riemann Sum

c)

Middle Riemann Sum

d)

Trapezoidal Sum

4.

For a function that is strictly decreasing, a right hand Riemann Sum is which of the following:

a)

Overestimate

b)

Underestimate

c)

Exact Solution

d)

Unable to Determine

5.

Find the right-hand Riemann Sum, with three sub-intervals indicated by the table.

a)

28

b)

16

c)

34

d)

23

6.

Find the Left-hand Riemann Sum, with three sub-intervals indicated by the table.

a)

28

b)

16

c)

34

d)

23

7.

Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.

a)

14

b)

7

c)

26

d)

11

8.

Use 3 trapezoids to determine the approximate area of the shaded area.

a)

12

b)

9

c)

10

d)

5

9.

Based on the table, use a trapezoidal sum of 4 sub-intervals to estimate the area under the curve.

a)

32.5

b)

40.5

c)

78

d)

160

10.

Select the correct integral notation for the summation below:

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{2}{n}\right)\left[2\left(4+\frac{2k}{n}\right)^2\right]$

a)

$\int_4^6\ \ 2x^2\ dx$

b)

$\int_0^2\ \ 2x\ dx$

c)

$\int_2^4\ \ 2x^2\ dx$

d)

$\int_4^6\ \ x^2\ dx$

11.

Select the correct integral notation for the summation below:

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{4}{n}\right)\left[\left(-5+\frac{4k}{n}\right)^2+3\left(-5+\frac{4k}{n}\right)+5\right]$

a)

$\int_{-5}^4\ \ -5x^2+x+5\ dx$

b)

$\int_{-5}^4\ \ x^2+3x+5\ dx$

c)

$\int_{-5}^{-1}\ \ x^2+3x+5\ dx$

d)

$\int_{-1}^{-5}\ \ x^2\ -3x\ +5\ dx$

12.

Select the correct integral notation for the summation below:

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[4\left(\frac{5k}{n}\right)\right]$

a)

$\int_4^5\ \ 4x\ dx$

b)

$\int_0^5\ \ 4x\ dx$

c)

$\int_0^5\ \ x\ dx$

d)

$\int_4^5\ \ x\ dx$

13.

Select the correct integral notation for the summation below:

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{\pi}{n}\right)\left[\cos\left(\pi+\frac{\pi k}{n}\right)\right]$

a)

$\int_0^{\pi}\ \ \pi\cos x\ dx$

b)

$\int_{\pi}^{2\pi}\ \ -\cos x\ dx$

c)

$\int_0^{\pi}\ \ \cos x\ dx$

d)

$\int_{\pi}^{2\pi}\ \ \cos x\ dx$

14.

Select the correct integral notation for the summation below:

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[1-5\left(-2+\frac{5k}{n}\right)^2\right]$

a)

$\int_{-2}^3\ \ 1-5x^{2\ }dx$

b)

$\int_{-2}^3\ \ 5x^2\ dx$

c)

$\int_1^6\ \ 5x^2\ dx$

d)

$\int_{-2}^1\ \ 1-5x^2\ dx$

15.

Select the correct integral notation for the summation below:

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{3}{n}\right)\left[\left(\frac{3k}{n}\right)^3\right]$

a)

$\int_3^6\ x^3\ dx$

b)

$\int_0^3\ x^3\ dx$

c)

$\int_0^3\ x\ dx$

d)

$\int_0^3\ x\ +\ 3\ dx$

16.

What is the upper limit?

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{-6}{n}\right)\left[\left(3-\frac{6k}{n}\right)^2-5\left(3-\frac{6k}{n}\right)+2\right]$

a)

$-3$

b)

$-6$

c)

$3$

d)

$5$

17.

What is the lower limit?

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{7}{n}\right)\left[4\left(-4+\frac{7k}{n}\right)+2\right]$

a)

$4$

b)

$2$

c)

$7$

d)

$-4$

18.

Select the correct summation notation for the integral below:

$\int_0^5\ x^4+2\ dx$

a)

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[2\left(\frac{5k}{n}\right)^4\right]$

b)

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[\left(5+\frac{5k}{n}\right)^4+2\right]$

c)

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\ \left(\frac{5}{n}\right)\left[\left(\frac{5k}{n}\right)^4+2\right]$

19.

Select the correct summation notation for the integral below:

$\int_{-2}^3\ \ \frac{1}{x^2+1}\ dx$

a)

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[\frac{1}{\left(-2+\frac{5k}{n}\right)+1}\right]$

b)

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[\left(-2+\frac{5k}{n}\right)^2+1\right]$

c)

$\lim_{n\rightarrow\infty}\sum_{k=1}^n\left(\frac{5}{n}\right)\left[\frac{1}{\left(-2+\frac{5k}{n}\right)^2+1}\right]$

20.

Which of the following definite integrals represent the area of the shaded region? (Scaled by ones)

a)

$\int_0^3\ x^2+3\ dx$

b)

$\int_1^3\ x^2+3\ dx$

c)

$\int_3^1\ x^2+3\ dx$

d)

$\int_1^3x^{2\ }+3\ dy$

21.

Which definite integral represents the area of the region enclosed by $y=\sqrt{9-x^2}$ and the x-axis.

a)

$\int_0^3\ \sqrt{9-x^2}dx$

b)

$\int_3^3\ \sqrt{9-x^2}dx$

c)

$\int_{-3}^3\ \sqrt{9-x^2}dx$

d)

$\int_3^{-3}\ \sqrt{9-x^2}dx$

22.

If $\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_5^5\ f\left(x\right)dx.$

a)

$-\pi$

b)

$0$

c)

$-0$

d)

$\pi$

23.

$If\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_5^4\ f\left(x\right)dx.$

a)

$0$

b)

$-1$

c)

$-\pi$

d)

$\pi$

24.

$\int_2^5\ f\left(x\right)dx=5\ and\ \ \int_4^5\ f\left(x\right)dx=\pi,\ find\ \int_2^4\ f\left(x\right)dx.$ If

a)

$\pi-5$

b)

$2$

c)

$5-\pi$

d)

$-\left(5-\pi\right)$

25.

For a function that is strictly increasing, a right hand Riemann Sum is which of the following:

a)

Overestimate

b)

Underestimate

c)

Unable to Determine

d)

Exact Solution

26.

Use the function values in the following table and the Trapezoidal Rule with n=6 to approximate the integral from x=0 to x=12.
x: 0 2 4 6 8 10 12
f(x): 7 11 20 25 18 14 9

a)

96

b)

102

c)

190

d)

192

27.

Evaluate the definite integral.

a)

3

b)

9/2

c)

9

d)

Not possible

28.

_{Evaluate the integral}

a)

30/3

b)

31/3

c)

29/3

d)

32/3

29.

a)

12/3

b)

6.5

c)

5.5

d)

11/3

30.

Find the area under a curve defined by the equation 5x⁴+3x+7 between the x values 0 and 4.

a)

1200

b)

1/12

c)

1134

d)

1076

31.

Using 5 subintervals, calculate the distance traveled using a left sum.

a)

360

b)

420

c)

396

d)

390

32.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

33.

Another word for 'integral' is .. .

a)

Constant

b)

Derivative

c)

Antiderivative

d)

Theorem

34.

Evaluate the definite integral.

a)

40

b)

20

c)

10

d)

Not possible

35.

Find the area under the curve y =3x²-2x from x= 1 to x =5.

a)

100

b)

99

c)

150

d)

152

36.

a)

a. 43

b)

b. 130/3

c)

c. 40

d)

d. 19/3

37.

a)

a. 24

b)

b. -8

c)

c. -10

d)

d. 22

38.

Find the Area under the curve.

a)

-500 ⁄ 3

b)

20 ⁄ 3

c)

500 ⁄ 3

d)

-20 ⁄ 3

39.

Evaluate the indefinite Integral

a)

-5/x⁵- 2/x³+ C

b)

-5/x³- 2/x⁴+ C

c)

5/x³- 2/x⁴+ C

d)

-5/x³- 2/x⁴

40.

a)

-4

b)

28

c)

40

d)

20

41.

a)

-1

b)

-2

c)

1/2

d)

-1/2

42.

a)

1/2

b)

3/2

c)

2

d)

3

43.

a)

y = 2

b)

y = 2(x - 1) - e

c)

y = -e(x - 1) + 2

d)

y = -2e(x - 1) + 2

44.

a)

-½x^-2 + C

b)

-⅖x^-5/2 + C

c)

2x^1/2 + C

d)

-2x^-1/2 + C

45.

a)

40

b)

32

c)

64

d)

Not possible

46.

Evaluate the definite integral.

a)

8 pi

b)

16 pi

c)

128 pi

d)

Not possible

47.

∫₁² (3x² + 4x³)dx

a)

a. 24

b)

b. -8

c)

c. -10

d)

d. 22

48.

∫₁³ 5x² dx

a)

a. 43

b)

b. 130/3

c)

c. 40

d)

d. 19/3

49.

Evaluate the indefinite integral.

a)

A

b)

B

c)

C

d)

D

50.

Evaluate the indefinite integral.

a)

A

b)

B

c)

C

d)

D

51.

Evaluate the indefinite integral.

a)

A

b)

B

c)

C

d)

D

52.

∫ t⁶ dt

a)

6t⁵

b)

6t⁵ + C

c)

1/7 t⁷ + C

d)

t⁷ + C

53.

∫ 4 dx

a)

0

b)

4t + C

c)

4x + C

d)

2x² + C

54.

a)

-(24/4)x⁴+C

b)

-4x⁶+C

c)

-4x⁵+C

d)

-24x⁶+C

55.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

56.

Evaluate the indefinite integral.

$\int_{ }^{ }\left(2x+2x^{-3}-6x^{-4}\right)dx$

a)

$x-x^{-3}+2x^4+C$

b)

$-2x+C$

c)

$x^2-x^{-2}+2x^{-3}+C$

d)

$2x^2+2x^{-2}-6x^{-3}+C$

57.

Evaluate the indefinite integral.

$\int_{ }^{ }\left(16x^3+5-6x^{-3}\right)dx$

a)

$4x^3+5+3x^{-3}+C$

b)

$4x^4+5x+3x^{-2}+c$

c)

$16x^4+5x-6x^{-2}+C$

d)

$15x+C$

58.

1.What should "u" equal in this integral?

a)

csc(x)

b)

csc²x

c)

sin(x)

d)

cos(x)

59.

a)

1/(e^cot(3x))+C

b)

(-e^-cot(3x))/3+C

c)

-1/(e^cot(3x))+C

d)

(e^-cot(3x))/3+C

60.

3. What should "u" equal in this integral?

a)

cos²x

b)

cosx

c)

sinx

d)

1-cos²x

61.

4. Solve for "c" given the initial condition.

a)

C=-7

b)

C=-11

c)

C=-4

d)

C=14/3

62.

What should "du" equal in this integral?

a)

tanxsecx dx

b)

secx dx

c)

sec²x dx

d)

tanx dx

63.

6. What should "u" equal in this integral?

a)

x

b)

(lnx)/x

c)

lnx

d)

sin(lnx)

64.

7. Solve for "c" given the initial condition.

a)

C=4

b)

C=Pi/4

c)

C=8

d)

C=-4

65.

a)

sec²x +C

b)

ln|cosx| +C

c)

-ln|sinx|+C

d)

-ln|cosx|+C

66.

10.Solve for "c" given the initial condition.

a)

C=3

b)

C=5

c)

C=0

d)

C=-1

67.

a)

sin x + C

b)

tan x + C

c)

sin² x + C

d)

-sin x + C

68.

∫xⁿ dx

a)

1/nxⁿ +c

b)

1/(n+1)xⁿ⁺¹ +c

c)

1/(n-1)x^n-1 +c

d)

1/n +c

69.

∫sec²x dx

a)

tanx +c

b)

-cotx +c

c)

secx +c

d)

-cscx +c

70.

∫₄¹⁰f(x)dx =

a)

2π + 3

b)

4π + 3

c)

2π - 3

d)

π - 3

71.

Solve by substitution

∫ x (x² + 7 )^(1/3) dx

a)

(3/4) ( x²+ 7 )^(4/3) + C

b)

(3/8) ( x²+ 7 )^(4/3) + C

c)

( x²+ 7 )^(4/3) + C

d)

(3/2) ( x²+ 7 )^(4/3) + C

72.

Solve using substitution

a)

(1/2)*sin(π^1/2)

b)

(1/2)*(cos(π^1/2)-1)

c)

π

d)

0

73.

a)

e^x+C

b)

e^sin(t)+C

c)

e^cos(t)+C

d)

-e^cos(t)+C

74.

Solve using integration by parts

a)

3t(e^2t)/2 - (e^2t)/4 + C

b)

3t(e^2t)⋅2 - 3(e^2t)⋅4 + C

c)

3(e^2t) - (e^2t)/4 + C

d)

3t(e^2t)/2 - 3(e^2t)/4 + C

75.

Let f be an even function

∫₀¹⁰ f(x) dx = 8

∫₀⁷ f(x) dx = 3

Find ∫₇¹⁰ f(x) dx

a)

11

b)

24

c)

5

d)

8/3

76.

a)

b)

c)

d)

e)

77.

Hasil dari $\int^{ }\left(2x+3\right)^2\ dx\ =\ ...$

a)

$\frac{4}{3}x^3-3x^2+9x+c$

b)

$\ \frac{4}{3}x^3+3x^2+9x\ +\ c$

c)

$\frac{4}{3}x^3-6x^2-9x+c\$

d)

$\frac{4}{3}x^3+6x^2+9x+c$

e)

$\frac{3}{4}x^3+6x^2-9x+c$

78.

$\int\ \frac{2x}{\sqrt{16-x^2}}dx$ can be solved by

a)

inverse trig integration

b)

the natural log pattern

c)

completing the square

d)

u-substitution

79.

$\int\ \frac{dx}{4+9x^{2\ }\ }$ can be solved by

a)

natural log pattern

b)

inverse trig integration

c)

partial fractions

d)

u-substitution

80.

$\int\ \frac{x^2}{x^2-x+1}dx$ must be solved by first

a)

completing the square

b)

finding the partial fractions

c)

using u-substitution

d)

performing long division

81.

$\int\ \frac{3x-1}{x^2+1}dx$ can be solved by first

a)

using inverse trig

b)

separating the integral into two fractions

c)

completing the square in the denominator

d)

using the natural log pattern

Unit 6 AB Test Review

Total questions: 81

Worksheet time: 4hrs 4mins

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