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B
3√25(e2π−1)
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C
3√25(e2π+1)
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D
−3√25(e2π+1)
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Solution
The correct option is D−3√25(e2π+1)
We have, ∫u.vdx=u∫vdx−∫(dudx∫vdx)dx .............. Integration by parts
Let I=∫2π0excos(π4+x2)dx =[excos(π4+x2)]2π0+12∫2π0exsin(π4+x2)dx .......... Using Integration by parts =[excos(π4+x2)]2π0+12[exsin(π4+x2)]2π0−14∫2π0excos(π4+x2)dx .......... Using Integration by parts