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Find the integral \int (\sin x)^{5/2}(\cos ^{3}x)dx

  • Option 1)

    2/7(\sin x)^{7/2} + C

  • Option 2)

    2/7(\sin x)^{7/2} \cos x + C

  • Option 3)

    2/7(\sin x )^{7/2} -2/9(\sin x )^{9/2}+ C

  • Option 4)

    2/7(\sin x )^{7/2} -2/5(\sin x )^{5/2}+ 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 (\sin x)^{5/2}(\cos ^{2}x) \cos dx

\Rightarrow \int (\sin x)^{5/2}(1-\sin ^{2}x) \cos dx

\Rightarrow \int ((\sin x)^{5/2}-(\sin ^{7/2}x)) \cos dx

\Rightarrow 2/7 (\sin x)^{7/2}- \frac{2}{9}(\sin x)^{9/2}+ C

 

 


Option 1)

2/7(\sin x)^{7/2} + C

Option 2)

2/7(\sin x)^{7/2} \cos x + C

Option 3)

2/7(\sin x )^{7/2} -2/9(\sin x )^{9/2}+ C

Option 4)

2/7(\sin x )^{7/2} -2/5(\sin x )^{5/2}+ C

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Aadil

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