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^{\u03c0\/2\u03b1}\u03b1\\sin\u03b1xdx\\\\\n=-\\cos(\\alpha*\\pi\/2\\alpha)+\\cos(0)=1"

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