# Find the integral $\int \sin x \cos^{3} xdx$ Option 1) $\frac{\cos ^{4}x}{4}+ C$ Option 2) $-\frac{\cos ^{4}x}{4}+ C$ Option 3) $\frac{\sin ^{4}x}{4}+ C$ Option 4) $\frac{-\sin x\cos ^{4}x}{4}+ C$

P Plabita

As we have learned

Special type of indefinite integration -

Integral of the form $(sin^{m}x)\left ( cos^{n} x\right ) \therefore \int \left ( sin^{m}xcos^{n}x \right )dx$

- wherein

Where  $m,n> 0$

In some case it may be  $m,n< 0$

put $\cos x = t ; -\sin x dx = dt$

$I = \int - t^{3}dt = \frac{-t^{4}}{4}+ C= \frac{-\cos ^{4}x}{4} + C$

Option 1)

$\frac{\cos ^{4}x}{4}+ C$

This is incorrect

Option 2)

$-\frac{\cos ^{4}x}{4}+ C$

This is correct

Option 3)

$\frac{\sin ^{4}x}{4}+ C$

This is incorrect

Option 4)

$\frac{-\sin x\cos ^{4}x}{4}+ C$

This is incorrect

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