`" If " f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is `A. x sin xB. x cos xC. sin x+x cos xD.

`" If " f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is `A. x sin xB. x c

1.	`" If " f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is `A. x sin xB. x cos xC. sin x+x cos xD.
Answer» Correct Answer - b ` f(x) = int_(0)^(x) t sin t dt` Using partial integration `f(x) =[int sin t dt -int [((d)/(dt)t) int sin t dt ]dt]_(0)^(x)` `= [t( -cos t)]_(0)^(x) - int_(0)^(x) (-cos t)dt` `=[-t cos t + sin t]_(0)^(x)` `rArr f(x) =-x cos x + sin x` Now differebntiate with respect to x . f(x) = -[{x(-sin x)}+cos x] +cos x `= sin x- cos x + cos x =x sin x`