Porisma

A hint to get started

Integrate a polynomial times sine twice by parts

Find ∫0πx2sin⁡(nx) dx\displaystyle\int_0^\pi x^2\sin(nx)\,dx, where nn is an even integer. Leave the answer in the form kπ2/nk\pi^2/n and determine kk. marks

[2018/IJC/I/2]

CJC · Review problems · Question 4

Reduce the polynomial degree by parts twice, then use sin(n pi)=0 and cos(n pi)=1.

Read the worked solution