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Question: If \(\int_{}^{\int\cos x}{x\sin}\) then \(A =\)...

If ∫∫cos⁡xxsin⁡\int_{}^{\int\cos x}{x\sin} then A=A =

A

sin⁡x+constant\sin x + \text{constant}

B

cos⁡x+constant\cos x + \text{constant}

C

Constant

D

None of these

Answer

sin⁡x+constant\sin x + \text{constant}

Explanation

Solution

Since ∫xsin⁡xdx=−xcos⁡x+A\int_{}^{}{x\sin xdx = - x\cos x + A}

⇒−xcos⁡x+sin⁡x+constant=−xcos⁡x+A\Rightarrow - x\cos x + \sin x + \text{constant} = - x\cos x + AEquating it, we get A=sin⁡x+constantA = \sin x + \text{constant}