Multiple Choice Questions on Evaluate the given Integral equation pi 0 4sin 3 theta d theta with respect to q ........ for NDA Exam Preparation

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Multiple Choice Questions

Evaluate the given Integral equation pi 0 4sin 3 theta d theta with respect to q ........

Mathematics (NDA) Integration
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    Evaluate the given Integral equation ?π0  4sin 3 θ dθ with respect to q?

    2/3

    Incorrect Answer

    4/3

    Incorrect Answer

    16/3

    Correct Answer

    26/3

    Incorrect Answer
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    Explanation:

    ?π0  4sin 3 θ dθ

    = ?π0  4(1-cos2θ)sin θ dθ

    Let cosθ   =t

    -sinθ dθ   =dt

    At θ=0  t=cos0  =1

    At θ=π,  t=cosπ=-1

    =  -  ?-11  4(1-t2)dt

    =4[  t-  t3 /3]-1 1

    =4[(1-1/3   ) -  (-1  + 1/3)]

    =4[2/3 +2/3]

    =16/3

    By: bhavesh kumar singh
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