Again from AITS PT 1 PAPER 1

Let f(x) = lim (n--->âˆž) cosx/[1+(tan^-1x)ⁿ]

Then the value of âˆ«[0--->âˆž] f(x)dx is equal to

(A) cos(tan1)

(B) sin(tan1)

(D) None

2 Answers

106

Asish Mahapatra ·2009-11-26 21:46:40

x=tan1 to x=inf... the integral is zero. (as taninv (x) becomes greater than 1 and to power inf. becomes inf.. and anything divided by inf = 0)

at x=0 to x<tan1 the integral is simply integral of cosx (as taninv(x) is less than 1 and less than 1 to power inf = 0)

i.e. sin(x) from x=0 to tan1

=> the reqd integral is sin(tan1)

Thanks Asish

U're ans is correct

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