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  • Can someone help me with this, - Integral Calculus - JEE Main-7

Evaluate \int (\sin x)^{4}(\cos x)^{-6}dx

  • Option 1)

    \frac{\sin ^{5}x(\cos x)^{-5}}{5}+ C

  • Option 2)

    \frac{\sin ^{5}x(\cos x)^{-7}}{35}+ C

  • Option 3)

    \frac{\sin ^{5}x(\cos x)^{-6}}{5}+ C

  • Option 4)

    \frac{(\sin x)^{5}}{5}+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

 

 \int \frac{\sin ^{4}x}{\cos ^{4}x}\times \frac{1}{\cos^{2}x}dx= \int \tan^{4}x \sec ^{2} x dx= \frac{\tan ^{5}x}{5}+ C

 

 

 

 


Option 1)

\frac{\sin ^{5}x(\cos x)^{-5}}{5}+ C

This is correct

Option 2)

\frac{\sin ^{5}x(\cos x)^{-7}}{35}+ C

This is incorrect

Option 3)

\frac{\sin ^{5}x(\cos x)^{-6}}{5}+ C

This is incorrect

Option 4)

\frac{(\sin x)^{5}}{5}+C

This is incorrect

Posted by

Aadil

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