Multiple Choice Questions on Integrate the given equation int pi 0 sin 3 theta d theta ........ for NDA Exam Preparation

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Multiple Choice Questions

Integrate the given equation int pi 0 sin 3 theta d theta ........

Mathematics (NDA) Integration
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    Integrate the given equation ∫π0  sin 3 θ dθ ?

    1/3

    Incorrect Answer

    -1/3

    Incorrect Answer

    4/3

    Correct Answer

    -4/3

    Incorrect Answer
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    Explanation:

    ?π0  sin 3 θ dθ

    = ?π0  (1-cos2θ)sin θ dθ

    Let cosθ   =t

    -sinθ dθ   =dt

    At θ=0  t=cos0  =1

    At θ=π,  t=cosπ=-1

    =  -  ?-11  (1-t2)dt

    =[  t-  t3 /3]-1 1

    =(1-1/3   ) -  (-1  + 1/3)

    =2/3 +2/3

    =4/3

    By: bhavesh kumar singh
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