What is the integral of x^2 sin(x) between the limits 0 and π/2
For this question, we have to integrate x2 multiplied by sin(x). For integrating a product, you must use a method called integration by parts. Without bogging ourselves down with the derivation, we know that integration by parts is given by: [write equation on whiteboard.] We have to pick either sin(x) or x2 to be u, and the other to be dv. The goal is to get rid of the x2 so that we can integrate the trigonometric function normally. This means we pick x2 to be u as we want to differentiate it, leaving sin(x) as dv to be integrated. We're then left with an integrated bit to sub the limits into and another product integral. We then perform integration by parts once more and are left with some terms and a simple standard integral. [finish question on whiteboard]
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