Free Printable Integration

1.

∫(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

2.

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)

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

3.

$\int\left(\frac{1}{x^2}+\frac{6}{x^3}\right)dx$

a)

$-x^{-1}-3x^{-2}+C$

b)

$\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$

c)

$-x^{-1}-3x^{-2}$

d)

$-x-3x^2+C$

4.

Integrate $\int_{ }^{ }\sin x\ dx$

a)

$=\tan x+c$

b)

$=-\cos x+c$

c)

$=-\sec x+c$

d)

$=\operatorname{cosec}\ x\ +c$

5.

∫⁰⁻₃ (4x)/(2x²+3)²dx [-3,0]

a)

-1/16

b)

-5/3

c)

-7/3

d)

2/7

6.

Find the integral:

a)

1/8(4x² + 3)⁴ + c

b)

1/2(4x² + 3)⁴ + c

c)

1/32(4x² + 3)⁴ + c

d)

1/4(4x² + 3)⁴ + c

7.

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

a)

$\frac{ax^{n+1}}{n+1}$

b)

$\frac{ax^{n-1}}{n-1}+\ c$

c)

$\frac{ax^{n+1}}{n}+\ c$

d)

$\frac{ax^{n+1}}{n+1}+\ c$

8.

$\int_{ }\left(2x+5\right)^3dx$

a)

$\frac{\left(2x+5\right)^4}{8}$

b)

$\frac{\left(2x+5\right)^4}{8}+c$

c)

$\frac{\left(2x-5\right)^4}{8}+c$

d)

$\frac{\left(2x+5\right)^3}{8}+c$

9.

$\int_{ }\frac{2}{3}\sqrt{x}dx$

a)

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

b)

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

c)

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

d)

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

10.

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

a)

$7$

b)

$8$

c)

$12$

d)

$x^3$

11.

Evaluate the integral $\int_0^2\ \frac{x^3\ +\ x^2}{x^2}\ dx$

a)

$2$

b)

$4$

c)

$6$

d)

$8$

12.

Evaluate the definite integral.

a)

3

b)

9/2

c)

9

d)

Not possible

13.

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

14.

Evaluate the definite integral.

a)

40

b)

20

c)

10

d)

Not possible

15.

Find the Area under the curve.

a)

-500 ⁄ 3

b)

20 ⁄ 3

c)

500 ⁄ 3

d)

-20 ⁄ 3

16.

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

a)

6

b)

20

c)

2

d)

24

17.

Find the area of the region bounded by the curves $y=x^2-5x$ and $y=25-x^2$ .

a)

$140\ \frac{6}{8}$

b)

$\frac{1125}{8}$

c)

$140$

d)

$\frac{1120}{8}$

Integration

Total questions: 17

Worksheet time: 1hrs 25mins

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