Differentiate $x \cos 3x$ with respect to $x$. Hence, show that \(\displaystyle\int_{0}^{\frac{\

Question

Differentiate $x \cos 3x$ with respect to $x$. Hence, show that $\displaystyle\int_{0}^{\frac{\pi}{9}} x \sin 3x \, \mathrm{d}x = \frac{\sqrt{3}}{18} - \frac{\pi}{54}$.

Accepted Answer

$\frac{\mathrm d}{\mathrm dx}(x\cos 3x)=\cos 3x-3x\sin 3x$ Hence: $\int_0^{\pi/9}x\sin 3x\,\mathrm dx=\frac{\sqrt3}{18}-\frac{\pi}{54}$

Techniques of Differentiation - Derivatives of Trigonometric Functions

Techniques of Differentiation - Derivatives of Trigonometric Functions

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