Free Printable Revision Topic 2 first part

1.

Find the integral:

a)

1/3(x⁴ + 3)³ + c

b)

1/12(x⁴ + 3)³ + c

c)

3/4(x⁴ + 3)³ + c

d)

1/4(x⁴ + 3)³ + c

2.

Integrate $\int\left(2x+1\right)^{10}\ dx$ with respect to x.

a)

$22\left(2x+1\right)^{11}+c$

b)

$\frac{1}{22}\left(2x+1\right)^{11}+c$

c)

$11\left(2x+1\right)^{10}+c$

d)

$\frac{1}{11}\left(2x+1\right)^{10}+c$

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.

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

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)

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

5.

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

a)

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

b)

$\frac{\ln2}{2}$

c)

$-\ln2$

d)

$\ln2$

6.

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

a)

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

b)

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

c)

$\ln3x+c$

d)

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

7.

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

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

8.

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

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)

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

9.

$\int_{ }\left(3\tan x+4\right)^5\sec^2x\ dx$ 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)

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

10.

$\int_{ }x\sin x\ dx$ 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)

$-x\cos x+\sin x$

Revision Topic 2 first part

Total questions: 10

Worksheet time: 20mins

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