Evaluate-sin-x-dx-

Question Number 31951 by NECx last updated on 17/Mar/18

E v a l u a t e \int \sin \sqrt{x} d x

Answered by mrW2 last updated on 17/Mar/18

u = \sqrt{x}

d u = \frac{d x}{2 \sqrt{x}} = \frac{d x}{2 u}

d x = 2 u d u

\int \sin \sqrt{x} d x

= \int 2 u \sin u d u

= - 2 \int u d \cos u

= - 2 [u \cos u - \int \cos u d u]

= - 2 [u \cos u - \sin u] + C

= 2 [\sin u - u \cos u] + C

= 2 [\sin \sqrt{x} - \sqrt{x} \cos \sqrt{x}] + C

Commented by mondodotto@gmail.com last updated on 19/Mar/18

thank you very much

Commented by NECx last updated on 20/Mar/18

t h a n k s s o m u c h!

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