Free Printable Trigonometric Integration

1.

$\int12\ \sin\ x\ dx\ =_{ }$

a)

$12\ \cos\ x\ +\ C$

b)

$-12\ \cos\ x\ +\ C$

c)

$\frac{1}{12}\cos\ x\ +\ C$

d)

$-\frac{1}{12}\cos\ x\ +\ C$

2.

$\int_{ }^{ }\sec^2\ 5x\ dx\ =\$

a)

$\frac{1}{5}\tan\ x\ +\ C$

b)

$5\tan\ 5x\ +\ C$

c)

$\frac{1}{5x}\tan\ 5x\ +\ C$

d)

$\frac{1}{5}\tan\ 5x\ +\ C$

3.

$\int_{ }^{ }\sin\ 9x\ dx$

a)

$\frac{1}{9}\cos\ 9x\ +\ C$

b)

$-\frac{1}{9}\cos\ 9x\ +\ C$

c)

$9\cos\ 9x\ +\ C$

d)

$-9\cos\ 9x\ +\ C$

4.

$\int_{ }^{ }4\ \sec^2\ x\ \ dx\ =$

a)

$4\ \tan\ 4x\ +\ C$

b)

$\tan4x\ +\ C$

c)

$4\ \tan\ x\ +\ C$

d)

$\frac{1}{4}\ \tan\ x\ +\ C$

5.

$\int_{ }^{ }7\cos\ x\ dx\ =\$

a)

$-7\ \sin\ x\ +\ C$

b)

$7\ \sin\ x\ +\ C$

c)

$\frac{1}{7}\ \sin\ x\ +\ C$

d)

$\ \sin7x\ +\ C$

6.

$\int_{ }2\sin\ 7x\ dx\ =$

a)

$7\cos\ 7x\ +\ C$

b)

$2\cos\ 7x\ +\ C$

c)

$\frac{2}{7}\cos\ 7x\ +\ C$

d)

$-\frac{2}{7}\cos\ 7x\ +\ C$

7.

$\int_{ }^{ }2\sec^2\ 5x\ dx\ =$

a)

$\frac{2}{5}\tan\ 5x\ +\ C\$

b)

$\frac{1}{5}\tan\ 5x\ +\ C\$

c)

$\frac{2}{5}\tan\ x\ +\ C\$

d)

$\frac{1}{5}\tan\ x\ +\ C\$

8.

$\int_{ }^{ }\sin\ \left(\ 5x\ +\ 12\ \right)\ dx\ =$

a)

$-\frac{1}{5}\cos\ \left(\ 5x\ +\ 12\ \right)\ +\ C$

b)

$\frac{1}{12}\cos\ \left(\ 5x\ +\ 12\right)+\ C$

c)

$\frac{1}{5}\cos\ \left(\ 5x\ +\ 12\right)+\ C$

d)

$\frac{1}{5}\cos\ \left(\ 5x\ \right)+\ C$

9.

$\int_{ }^{ }\cos\ \left(2-7x\right)\ dx\ =$

a)

$\frac{1}{7}\sin\ \left(\ 2-7x\right)\ +\ C$

b)

$-\frac{1}{7}\sin\ \left(\ 2-7x\right)\ +\ C$

c)

$-\frac{1}{2}\sin\ \left(\ 2-7x\right)\ +\ C$

d)

$-\frac{2}{7}\sin\ \left(\ 2-7x\right)\ +\ C$

10.

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

a)

$\frac{2}{6}\sin\ \left(6+3x\right)\ +\ C$

b)

$\frac{1}{6}\sin\ \left(6+3x\right)\ +\ C$

c)

$\frac{2}{3}\sin\ \left(6+3x\right)\ +\ C$

d)

$\frac{2}{3x}\sin\ \left(6+3x\right)\ +\ C$

11.

Evaluate: $∫(15-\csc^2x)dx$

a)

$15+\cot x+C$

b)

$15x+\cot x+C$

c)

$15x-\cot x+C$

12.

Evaluate: $∫(15M^4-5\sec⁡M\tan⁡M)dM$

a)

$15M^4-5\sec M+C$

b)

$3M^5-5\sec M+C$

c)

$3M^5+5\sec M+C$

13.

Evaluate: $∫(5\sin⁡x-4\cos⁡x)dx$

a)

$5\sin⁡x-4\cos⁡x+C$

b)

$-5\cos⁡x-4\sin⁡x+C$

c)

$5\cos⁡x+4\sin⁡x+C$

14.

Evaluate: $∫\sin⁡θ\cot⁡θdθ$

a)

$\sin⁡θ+C$

b)

$\cos⁡θ+C$

c)

$\cot⁡θ+C$

15.

Evaluate: $∫\tan⁡\beta\sec⁡\beta\csc⁡\beta\ d\beta$

a)

$\sec^2⁡\beta+C$

b)

$\tan⁡\beta+C$

c)

$\csc^2⁡\beta+C$

16.

Evaluate: $∫\frac{\sec⁡u}{\cot u}du$

a)

$\sec⁡u\tan u+C$

b)

$\sec u+C$

c)

$\tan u+C$

17.

$\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$

a)

$\tan\ x\ \ +\ c$

b)

$\frac{1}{5}\tan\ x\ \ +\ c$

c)

$\frac{1}{5}\tan\ 5x\ \ +\ c$

d)

$\frac{1}{5}\tan^2\ 5x\ \ +\ c$

18.

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)

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

19.

$\int_{ }^{ }\tan xdx$

a)

cotx + C

b)

$\sec^2x+C$

c)

ln|secx| +C

d)

ln|cosx| +C

20.

$\int_{ }^{ }\sin\left(5x\right)dx$

a)

$-\frac{1}{5}\cos\left(5x\right)+C$

b)

$\frac{1}{5}\cos\left(5x\right)+C$

c)

5cos(5x) + C

d)

None of the above

21.

$\int_{ }^{ }\sec x\tan xdx$

a)

$\sec^2x$

b)

$\sec^2x\ +\ C$

c)

-secx + C

d)

secx + C

22.

$\int_{ }^{ }\csc^2xdx$

a)

2cscxcotx + C

b)

-cot(x) + C

c)

cot(x) + C

d)

None of the above

23.

$\int_{ }^{ }\cot^2xdx$

a)

$-\csc x\ +C$

b)

$-\csc^2x\ +C$

c)

$-\cot x\ -\ x\ +\ C$

d)

$-\cot x\ +\ x\ +\ C$

24.

$\int_{ }^{ }\csc x\cot xdx$

a)

$\csc x$

b)

$-\csc x$

c)

$\cot x$

d)

$-\cot x$

e)

None of the above

25.

Integrate $\int_{ }^{ }\left(\frac{1-\sin x}{\cos^2x}\right)dx$

a)

$\tan x-\sec x+c$

b)

$\tan x+\sec x+c$

c)

$\cot x-\operatorname{cosec}x+c$

d)

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

26.

Integrate $\int_{ }^{ }\left(\frac{\cos2x}{\cos^2x}\right)dx$

a)

$2x-\tan x+c_{ }$

b)

$2x+\tan x+c$

c)

$x-\tan x+c$

d)

$x+\tan x+c$

27.

Integrate $\int_{ }^{ }\left(\frac{\cos^2x}{\sin^2x}\right)dx$

a)

$-\cot x-x+c$

b)

$\cot x+x+c$

c)

$-\cot x+x+c$

d)

$\cot x-x+c$

28.

Integrate $\int_{ }^{ }\left(\cos x-\sin x\right)^2dx$

a)

$x+\frac{1}{2}\cos2x+c$

b)

$x-\frac{1}{2}\cos2x+c$

c)

$x+\cos2x+c$

d)

$x-\cos2x+c$

29.

Integrate $\int_{ }^{ }\frac{\left(1+\cos x\right)^2}{\sin^2x}dx$

a)

$-2\cot x-x-2\operatorname{cosec}x+c$

b)

$2\cot x-x+2\operatorname{cosec}x+c$

c)

$-2\cot x-x+2\operatorname{cosec}x+c$

d)

$2\cot x-x-2\operatorname{cosec}x+c$

30.

Integrate $\int_{ }^{ }\left(\cot x-\tan x\right)^2dx$

a)

$-\cot x-4x+\tan x+c$

b)

$-\cot x-4x-\tan x+c$

c)

$\cot x-4x-\tan x+c$

d)

$\cot x-4x+\tan x+c$

31.

Integrate $\int_{ }^{ }\left(\cos x-\sec x\right)^2dx$

a)

$-\frac{3}{2}x+\frac{1}{4}\sin2x+\tan x+c$

b)

$-\frac{3}{2}x+\frac{1}{2}\sin2x+\tan x+c$

c)

$-\frac{3}{2}x-\frac{1}{4}\sin2x+\tan x+c$

d)

$-\frac{3}{2}x-\frac{1}{2}\sin2x+\tan x+c$

32.

Integrate $\int_{ }^{ }\left(\frac{\cos2x}{1-\cos^22x}\right)dx$

a)

$-\frac{1}{2}\operatorname{cosec}2x+c$

b)

$\frac{1}{2}\operatorname{cosec}2x+c$

c)

$-\frac{1}{2}\sec2x+c$

d)

$\frac{1}{2}\sec2x+c$

33.

$\int_{ }^{ }\operatorname{cosec}\left(4x\right)\cot\left(4x\right)dx$

a)

$4\operatorname{cosec}\left(4x\right)+c$

b)

$-\frac{\operatorname{cosec}\left(4x\right)}{4}+c$

c)

$-4\operatorname{cosec}\left(4x\right)+c$

d)

$\operatorname{cosec}\left(4\right)+c$

34.

$\int_{ }\sin\left(\frac{x}{2}\right)\ dx$

a)

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

b)

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

c)

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

d)

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

Trigonometric Integration

Total questions: 34

Worksheet time: 17mins

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