Answer to Question #229214 in Chemical Engineering for Lokika

Chemical Engineering

Question #229214

Evaluate ∫0^{π/2α}αsinαxdx,α>0 by using Leibniz formula.`

Expert's answer

The Leibniz formula says

\int_{a}^b f(x)dx=F(b)-F(a)

We get

\int_0^{π/2α}α\sinαxdx\\ =-\cos(\alpha*\pi/2\alpha)+\cos(0)=1

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