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Question

Solve π20sinϕcos5ϕdϕ.

A
64231
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B
24231
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C
54231
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D
None of these
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Solution

The correct option is A 64231
Let

I=π20sinϕcos5ϕdϕ=π20sinϕcos4ϕcosϕdϕ=π20sinϕ(1sin2ϕ)2cosϕdϕputt=sinϕdtdϕ=cosϕdt=cosϕdϕWhenϕ=0,t=0whenϕ=π2,t=1I=10t(1t2)2dt=10t(12t2+t4)dt=10t12+t922t52dt=23t32+211t11247t7210=23+21147=154+421323×11×7=64231

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