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  4. If y = 2 sin x + sin 2x for 0 le x le2π, then the area enclosed by the curve and x-axis is

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Q. If $y = 2 \,sin \,x + sin \,2x$ for $0 \,\le x \,\le2\pi$, then the area enclosed by the curve and x-axis is

Application of Integrals

Solution:

$A=\int\limits_{0}^{2\pi} 2\,sin \,x \,dx+\int\limits_{0}^{2\pi} sin\,2x\,dx$

image
$\Rightarrow \quad A=2\int\limits_{0}^{\pi}2 sin \,x\, dx+0$
$=4\left[-cos\,x\right]_{0}^{\pi}$

$=-4\left[-1-1\right] = 8 $ sq. units