Differentiate $y = 2x \sin x \cos x$ with respect to $x$. Hence, find \(\displaystyle\displaysty

Question

Differentiate $y = 2x \sin x \cos x$ with respect to $x$. Hence, find $\displaystyle\displaystyle \displaystyle\int_{\frac{\pi}{4}}^{0} \frac{x \cos 2x}{3} \, \mathrm{d}x$.

Accepted Answer

$\frac{\mathrm dy}{\mathrm dx}=\sin 2x+2x\cos 2x$ Hence: $\int_{\pi/4}^{0}\frac{x\cos 2x}{3}\,\mathrm dx=\frac1{12}-\frac{\pi}{24}$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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