Free Printable Integration

1.

Given $\frac{d}{dx}\left(\frac{2}{x-3}\right)=g\left(x\right)$ , find $\int_{ }^{ }g\left(x\right)dx$ .

a)

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

b)

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

c)

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

d)

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

2.

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

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)

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

3.

$\int_{ }\frac{8}{x^5}dx$

a)

$-\frac{2}{x^4}$

b)

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

c)

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

d)

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

4.

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

a)

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

b)

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

c)

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

d)

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

5.

$\int_{ }8e^{7+2x}dx$

a)

$8\left(\frac{e^{7+^{ }2x}}{2\left(\ln e\right)}\right)$

b)

$8\left(\frac{e^{7+^{ }2x}}{\left(\ln e\right)}\right)+c$

c)

$8\left(\frac{e^{7+^{ }2x}}{2\left(\ln e\right)}\right)+c$

d)

$\left(\frac{e^{7+^{ }2x}}{2\left(\ln e\right)}\right)+c$

6.

$\int_1^24^xdx$

a)

$\frac{12}{\ln4}$

b)

$\frac{\ln4}{12}$

c)

2.3336

d)

4.114

7.

$\int_{ }\frac{4}{5x-6}dx$

a)

$4\ln\left|5x-6\right|+c$

b)

$\frac{4}{5}\ln\left|5x-6\right|+c$

c)

$\frac{4}{5}\ln\left|5x-6\right|$

d)

$\ln\left|5x-6\right|+c$

8.

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

a)

$-\frac{\ln2}{2}$

b)

$\frac{\ln2}{2}$

c)

$-\ln2$

d)

$\ln2$

9.

$\int_{ }\frac{2x+1}{x^2+x+1}dx$ by using method of substitution.

a)

$\ln\left|u\right|$

b)

$\ln\left|u\right|+c$

c)

$\ln\left|x^2+x+1\right|+c$

d)

$\ln\left|x^2+x+1\right|$

10.

$\int_{ }\frac{\left(\ln3x\right)^4}{x}dx$ by using method of substitution.

a)

$\frac{u^5}{5}$

b)

$\frac{\left(\ln3x\right)^5}{5}+c$

c)

$\ln3x+c$

d)

$\frac{\ln3x}{5}+c$

11.

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

a)

$\frac{-\cos\left(2x+3\right)}{2}$

b)

$-\cos\left(2x+3\right)+c$

c)

$\frac{-\cos\left(2x+3\right)}{2}+c$

d)

$\frac{\cos\left(2x+3\right)}{2}+c$

12.

$\int_{ }\left(3\tan x+4\right)^5\sec^2x\ dx$ by using method of substitution.

a)

$\left(3\tan x\ +4\right)^6+c$

b)

$\frac{\left(3\tan x\ +4\right)^6}{6}$

c)

$\frac{\left(3\tan x\ -4\right)^6}{6}+c$

d)

$\frac{\left(3\tan x\ +4\right)^6}{6}+c$

13.

$\int_{ }xe^x\ dx$ by using integration by parts.

a)

$e^x\left(x-1\right)+c$

b)

$xe^x+e^x+c$

c)

$xe^x+c$

d)

$xe^x-e^x$

14.

$\int_{ }x\sin x\ dx$ by using integration by parts.

a)

$x\cos x+\sin x+c$

b)

$-x\cos x+\sin x+c$

c)

$-x\sin x+\cos x+c$

d)

$-x\cos x+\sin x$

15.

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)

$\frac{1120}{8}$

16.

Given that R is the area bounded by the curve $y^2=12\left(3-x\right)$ and the axes in the first quadrant. Find the volume of the solid of revolution obtained by revolving the region R about the $x-axis.$

a)

$52\pi$

b)

$53\pi$

c)

$54\pi$

d)

$55\pi$

Integration

Total questions: 16

Worksheet time: 35mins

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