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Question

Find the integral of the given function w.r.t - x

y=sin2x2x


A

12x3+13sin 3x+c

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B

12x14sin 2x+c

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C

12x14sin x+c

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D

None of these

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Solution

The correct option is B

12x14sin 2x+c


I=ydx=sin2x2xdx

Let u=x,dudx=12x

du=dx2x ......(i)

I=sin2u du(substituting (i))

= 1cos 2u2du(cos2a=12sin2a)

= 12du12cos2udu

Let t=2udtdu=2du=dt2

I=12du12cost dt2

= 12u+c114cos t dt

= 12u+c114sin t+c2

= 12u14sin t+c3

= 12x14sin 2u+c3

= 12x14sin 2x+c3


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