It is given that $\mathrm{f}\left( x \right)=\sin 2mx+\sin 2nx$, where $m$ and $n$ are positive inte

Question

It is given that $\mathrm{f}\left( x ight)=\sin 2mx+\sin 2nx$, where $m$ and $n$ are positive integers and $m
e n$. Find $\displaystyle\int{\sin 2mx\sin 2nx\mathrm{ d}x}$. [3] Find $\displaystyle\int_{0}^{\pi }{{{\left( \mathrm{f}\left( x ight) ight)}^{2}}\mathrm{d}x}$ . [5]

Accepted Answer

(i) $-\frac{\sin \left[ \left( 2m+2n \right)x \right]}{4\left( m+n \right)}+\frac{\sin \left[ \left( 2m-2n \right)x \right]}{4\left( m-n \right)}+C$ (ii) $\pi $

N2017 P1 Q7

N2017 P1 Q7

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