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Question
If Φ(x)=limnxnxnxn+xn,0<x<1,ϵN, then (sin1x)(Φ(x))dx is equal to
Options:
A .  x sin−1(x)+√1−x2+C
B .  −(x sin−1(x)+√1−x2)
C .  x sin−1 x+√1−x2+C
D .  None of these
Answer: Option A
:
A
We have ϕ(x)=limnx2n1x2n+1=1,0<x<1sin1x.ϕ(x)dx=sin1xdx=[xsin1x+1x2]+c

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