It is given that $\mathrm{f}(x)=\sin 4px+\cos 4qx$, where $p$ and $q$ are positive integers and $p

Question

It is given that $\mathrm{f}(x)=\sin 4px+\cos 4qx$, where $p$ and $q$ are positive integers and $p
e q$. Find $\displaystyle\int{\,\sin 4px\cos 4qx\,\,\mathrm{d}x}$. [2] Find $\displaystyle\int
olimits_{0}^{\frac{\pi }{2}}{{{\left( \mathrm{f}(x) ight)}^{2}}\,\mathrm{d}x}$. [5]

Accepted Answer

(i) $-\dfrac{1}{8(p+q)}\cos[4(p+q)x] - \dfrac{1}{8(p-q)}\cos[4(p-q)x] + C$; (ii) $\dfrac{\pi}{2}$

2018 NYJC J2 BT Q1 [Modified]

2018 NYJC J2 BT Q1 [Modified]

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