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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

 

Answers (1)

best_answer

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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