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" If" f(x) =int_(0)^(x)" t sin t dt tehn " f(x) is |
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Answer» x SIN x 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` |
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