Q

# Tell me? - Integral Calculus - JEE Main-9

Evaluate $\int \sin ^{4}xdx$

• Option 1)

$\frac{1}{8}+\frac{\sin 4x}{32}+ \frac{\sin 2x}{2}+C$

• Option 2)

$\frac{1}{8}-\frac{\sin 4x}{32}-\frac{\sin 2x}{2}+C$

• Option 3)

$\frac{1}{8}-\frac{\sin 4x}{32}+ \frac{\sin 2x}{2}+C$

• Option 4)

none of these

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As we have learned

Integration of trigonometric function of power m -

$\int sin^{m}xdx$    and

$\int cos^{m}xdx$

- wherein

for $m=2$,

$sin^{2}x=\frac{1-cos 2x}{2}$

for $m=3$,

$sin3x=3sinx-4sin^{3}x$

$\int \sin ^{4} dx = \int \left ( 1-\frac{\cos 2x}{2} \right )$

$=\int \left ( 1/4+ \frac{\cos 2x}{4}- \cos 2x \right )dx$

$=\int \left ( 1/4+ \frac{1+ \cos 4x}{8}- \cos 2x \right )dx$

$1/8 - \frac{\sin 4x}{32 }- \frac{\sin 2x}{2}+ C$

Option 1)

$\frac{1}{8}+\frac{\sin 4x}{32}+ \frac{\sin 2x}{2}+C$

This is incorrect

Option 2)

$\frac{1}{8}-\frac{\sin 4x}{32}-\frac{\sin 2x}{2}+C$

This is correct

Option 3)

$\frac{1}{8}-\frac{\sin 4x}{32}+ \frac{\sin 2x}{2}+C$

This is incorrect

Option 4)

none of these

This is incorrect

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