Free Printable 11-5 Definite Integration

1.

∫_₀^²(3x² - 2x)dx ?

a)

8

b)

4

c)

-8

d)

-4

2.

Evaluate the definite integral.

a)

8 pi****

b)

16 pi

c)

128 pi

d)

Not possible

3.

a)

⅝

b)

-⅝

c)

⅜

d)

45/16

4.

Given that $∫_2^5g(x)dx=-7$ and $\int_5^9\ g\left(x\right)dx=10$

Find the value of $∫_2^9g(x)dx$

a)

-17

b)

3

c)

-3

d)

17

5.

Value of integral

$\int_{ }^{ }3x^2\cos\ x^3\ dx$

a)

$\cos\ x^3+c$

b)

$\sin\ x^3+c$

c)

$\frac{x^3}{3}+c$

d)

$3x^2+c$

6.

$\int_0^{\pi}\left|Sin\ x\right|\ dx$

a)

0

b)

1

c)

2****

d)

3

7.

Integrate $\sqrt{x}$ with respect to x

a)

$x^{\frac{1}{2}}+c$

b)

$\frac{1}{2}x^{-\frac{1}{2}}+\ c$

c)

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

d)

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

8.

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

a)

$\frac{3x^2}{2}$

b)

$\frac{3x^2}{2}+7x+c$

c)

$\frac{x^4}{8}+7x+c$

d)

$\frac{x^4}{8}+c$

9.

Which of the following is the indefinite integral of $\frac{3}{x^4}\ \ ?$

a)

$-\frac{1}{x^3}+\ c$

b)

$\frac{3}{5x^5}+\ c$

c)

$-\frac{12}{x^5}+\ c$

d)

$\frac{1}{x^3}+\ c$

10.

Integrate $\sin\left(\frac{x}{2}\right)$ with respect to x

a)

$\cos\left(\frac{x}{2}\right)\ +\ c$

b)

$-2\cos\left(\frac{x}{2}\right)\ +\ c$

c)

$-\cos\left(\frac{x}{2}\right)\ +\ c$

d)

$-\frac{1}{2}\cos\left(\frac{x}{2}\right)\ +\ c$

11.

$\int6x\left(x+2\right)dx$

a)

$6x^2+12x+C$

b)

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

c)

$3x^2+6x+C$

d)

$2x^3+6x^2+C$

12.

$\int0dx$

a)

$\frac{1}{x}+C$

b)

$Not\ Possible$

c)

$x+C$

d)

$C$

13.

Find the area of the shaded region.

a)

-7/3

b)

-13/3

c)

13/3

d)

7/3

14.

Evaluate the definite integral using the First Fundamental Theorem of Calculus.

a)

-4

b)

-2

c)

4

d)

5

15.

HINT: remember exponent laws and fraction rules :)

a)

12/3

b)

6.5

c)

5.5

d)

11/3

16.

∫ 6 x (x² +1 )² dx

a)

( x² + 1)³ + C

b)

3 ( x² + 1)³ + C

c)

( x² + 1)¹ + C

d)

6 ( x² + 1)³ + C

17.

What should be used for u in the integral?

a)

no u needed

b)

4t²

c)

t³

d)

1/4t²

18.

Evaluate the definite integral.

a)

3

b)

9/2

c)

9

d)

-9/2

19.

a)

-8

b)

8

c)

-2

d)

2

20.

a)

a. 43

b)

b. 130/3

c)

c. 40

d)

d. 19/3

21.

_{Evaluate the integral}

a)

30/3

b)

31/3

c)

29/3

d)

32/3

22.

a)

a. 24

b)

b. -8

c)

c. -10

d)

d. 22

23.

a)

4/3

b)

5/3

c)

7/3

d)

19/3

e)

25/3

24.

a)

25/2

b)

21/2

c)

61/6

d)

21

25.

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

26.

Using the areas of each region given
$\int_a^df\left(x\right)=$

a)

6

b)

20

c)

2

d)

24

27.

the definite integral from x = 1 to x = 3 of ∫2xcos(x²)dx is equal to the following

a)

the definite integral from x = 1 to

x = 9 of ∫sin(u) du

b)

the definite integral from x = 1 to x = 9 of ∫cos(u) du ****

c)

the definite integral from x = 1 to x = 3 of ∫cos(u) du

d)

does not exist

28.

Evaluate in terms of area

∫₀² f(x) dx

a)

4

b)

-4

c)

4 + 2π

d)

-4 - 2π

29.

Evaluate in terms of area

∫₀¹⁴ f(x) dx

a)

10π + 4

b)

8π - 4

c)

6π + 4

d)

6π - 4

11-5 Definite Integration

Total questions: 29

Worksheet time: 7hrs 32mins

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