1.

" If" f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is

Answer»

x SIN x
x cos x
sin x+xcos x

Solution :` f(x) = int_(0)^(x) TSIN t DT`
Usingpartialintegration
`f(x) =[intsintdt -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`
Nowdifferebntiate withrespect to x .
f(x) = -[{x(-sin x)}+cos x] +cos x
`= sin x- cos x + cos x =x sin x`


Discussion

No Comment Found

Related InterviewSolutions