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  • Choose the correct answer in Exercises 9 and 10. If f (x) = Integral 0 to x t sin t dt, then f'(x) is (A) (B) (C) (D)

Choose the correct answer in Exercises 9 and 10.

    Q10.    If f(x) = \int_0^x t \sin t dt, then f'(x) is

                (A)    \cos x + x\sin x

                (B)    x\sin x

                (C)    x\cos x

                (D)    \sin x + x\cos x

Answers (1)

best_answer

The correct answer is (B) = x\sin x

f(x) = \int_0^x t \sin t dt
by using by parts method,
\\=t\int \sin t dt - \int (\frac{d}{dt}t\int \sin t dt)dt\\ =[t(-\cos t )+\sin t]^x_0

f(x)= -x\cos x+sinx
So, f'(x)= -\cos x+x\sin x+\cos x\\ =x\sin x 

Posted by

manish

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