∫ 12 sin ⁡ x d x = \int12\ \sin\ x\ dx\ =_{ } ∫ 1 2 sin x d x =

− 12 cos ⁡ x + C -12\ \cos\ x\ +\ C − 1 2 cos x + C

12 cos ⁡ x + C 12\ \cos\ x\ +\ C 1 2 cos x + C

1 12 cos ⁡ x + C \frac{1}{12}\cos\ x\ +\ C 1 2 1 cos x + C

− 1 12 cos ⁡ x + C -\frac{1}{12}\cos\ x\ +\ C − 1 2 1 cos x + C

∫ sin ⁡ 9 x d x \int_{ }^{ }\sin\ 9x\ dx ∫ sin 9 x d x

− 1 9 cos ⁡ 9 x + C -\frac{1}{9}\cos\ 9x\ +\ C − 9 1 cos 9 x + C

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

∫ 7 cos ⁡ x d x = \int_{ }^{ }7\cos\ x\ dx\ =\ ∫ 7 cos x d x =

7 sin ⁡ x + C 7\ \sin\ x\ +\ C 7 sin x + C

− 7 sin ⁡ x + C -7\ \sin\ x\ +\ C − 7 sin x + C

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

sin ⁡ 7 x + C \ \sin7x\ +\ C sin 7 x + C

∫ 2 sin ⁡ 7 x d x = \int_{ }2\sin\ 7x\ dx\ = ∫ 2 sin 7 x d x =

− 2 7 cos ⁡ 7 x + C -\frac{2}{7}\cos\ 7x\ +\ C − 7 2 cos 7 x + C

7 cos ⁡ 7 x + C 7\cos\ 7x\ +\ C 7 cos 7 x + C

2 cos ⁡ 7 x + C 2\cos\ 7x\ +\ C 2 cos 7 x + C

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

∫ sin ⁡ ( 5 x + 12 ) d x = \int_{ }^{ }\sin\ \left(\ 5x\ +\ 12\ \right)\ dx\ = ∫ sin ( 5 x + 1 2 ) d x =

− 1 5 cos ⁡ ( 5 x + 12 ) + C -\frac{1}{5}\cos\ \left(\ 5x\ +\ 12\ \right)\ +\ C − 5 1 cos ( 5 x + 1 2 ) + C

1 12 cos ⁡ ( 5 x + 12 ) + C \frac{1}{12}\cos\ \left(\ 5x\ +\ 12\right)+\ C 1 2 1 cos ( 5 x + 1 2 ) + C

1 5 cos ⁡ ( 5 x + 12 ) + C \frac{1}{5}\cos\ \left(\ 5x\ +\ 12\right)+\ C 5 1 cos ( 5 x + 1 2 ) + C

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

∫ cos ⁡ ( 2 − 7 x ) d x = \int_{ }^{ }\cos\ \left(2-7x\right)\ dx\ = ∫ cos ( 2 − 7 x ) d x =

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

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

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

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

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

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

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

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

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

Evaluate: ∫ ( 5 sin ⁡ ⁡ x − 4 cos ⁡ ⁡ x ) d x ∫(5\sin⁡x-4\cos⁡x)dx ∫ ( 5 sin ⁡ x − 4 cos ⁡ x ) d x

− 5 cos ⁡ ⁡ x − 4 sin ⁡ ⁡ x + C -5\cos⁡x-4\sin⁡x+C − 5 cos ⁡ x − 4 sin ⁡ x + C

5 sin ⁡ ⁡ x − 4 cos ⁡ ⁡ x + C 5\sin⁡x-4\cos⁡x+C 5 sin ⁡ x − 4 cos ⁡ x + C

5 cos ⁡ ⁡ x + 4 sin ⁡ ⁡ x + C 5\cos⁡x+4\sin⁡x+C 5 cos ⁡ x + 4 sin ⁡ x + C

Evaluate: ∫ sin ⁡ ⁡ θ cot ⁡ ⁡ θ d θ ∫\sin⁡θ\cot⁡θdθ ∫ sin ⁡ θ cot ⁡ θ d θ

cos ⁡ ⁡ θ + C \cos⁡θ+C cos ⁡ θ + C

sin ⁡ ⁡ θ + C \sin⁡θ+C sin ⁡ θ + C

cot ⁡ ⁡ θ + C \cot⁡θ+C cot ⁡ θ + C

Evaluate: ∫ sec ⁡ ⁡ u cot ⁡ u d u ∫\frac{\sec⁡u}{\cot u}du ∫ cot u sec ⁡ u d u

sec ⁡ u + C \sec u+C sec u + C

sec ⁡ ⁡ u tan ⁡ u + C \sec⁡u\tan u+C sec ⁡ u tan u + C

tan ⁡ u + C \tan u+C tan u + C

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

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

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

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

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

∫ sin ⁡ ( 5 x ) d x \int_{ }^{ }\sin\left(5x\right)dx ∫ sin ( 5 x ) d x

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

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

∫ csc ⁡ x cot ⁡ x d x \int_{ }^{ }\csc x\cot xdx ∫ csc x cot x d x

− csc ⁡ x -\csc x − csc x

− cot ⁡ x -\cot x − cot x

∫ cosec ⁡ ( 4 x ) cot ⁡ ( 4 x ) d x \int_{ }^{ }\operatorname{cosec}\left(4x\right)\cot\left(4x\right)dx ∫ c o s e c ( 4 x ) cot ( 4 x ) d x

− cosec ⁡ ( 4 x ) 4 + c -\frac{\operatorname{cosec}\left(4x\right)}{4}+c − 4 c o s e c ( 4 x ) + c

4 cosec ⁡ ( 4 x ) + c 4\operatorname{cosec}\left(4x\right)+c 4 c o s e c ( 4 x ) + c

− 4 cosec ⁡ ( 4 x ) + c -4\operatorname{cosec}\left(4x\right)+c − 4 c o s e c ( 4 x ) + c

cosec ⁡ ( 4 ) + c \operatorname{cosec}\left(4\right)+c c o s e c ( 4 ) + c

∫ sin ⁡ ( x 2 ) d x \int_{ }\sin\left(\frac{x}{2}\right)\ dx ∫ sin ( 2 x ) d x

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

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

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

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

Trigonometric Integration

Quiz

•

Mathematics

•

11th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF.TF.B.7, HSA.APR.D.6, HSA.SSE.B.3

Standards-aligned

Harry Williams

Used 23+ times

FREE Resource

34 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

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

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

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

$\tan4x\ +\ C$

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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

$\ \sin7x\ +\ C$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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

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

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

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

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

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

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

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

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

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