Choose the correct answer .If `f(x)=int_0^x tsint dt`, then `f^(prime)(x)`is

Options

A. (A) `cos x + x sin x`
B. (B) `x sin x`
C. (C) `x cos x`
D. (D) `sin x+ x cos x`

Answer

B

Explanation

Option `B` is the correct answer


Given `f(x)=int_0^x tsint dt`


integrating by parts, we obtain


`f(x)=tint_0^x(sint)dt-int_0^x{(d/(dt)(t))intsintdt}dt`


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