Answer to Question #229214 in Chemical Engineering for Lokika

Question

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

Answer 1

The Leibniz formula says

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

We get

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