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" If "I=int(1)/(2p)sqrt((p-1)/(p+1))dp=f...

" If "I=int(1)/(2p)sqrt((p-1)/(p+1))dp=f(p)+c," then "f(p)" is equal to "

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Let p(x) be a function defined on R such that p'(x)=p'(1-x) for all x epsilon[0,1],p(0)=1 and p(1)=41 . Then int_(0)^(1)p(x)dx is equals to (a) 42 (b) sqrt(41) (c) 21 (d) 41