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Question

If Φ(x)=limnxnxnxn+xn,0<x<1,ϵN, then (sin1x)(Φ(x))dx is equal to

A
x sin1(x)+1x2+C
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B
(x sin1(x)+1x2)
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C
x sin1 x+1x2+C
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D
None of these
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Solution

The correct option is A x sin1(x)+1x2+C
We have ϕ(x)=limnx2n1x2n+1=1,0<x<1sin1x.ϕ(x) dx=sin1x dx=[x sin1 x+1x2]+c

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