The area bounded by the curves $y-1=\cos x, y=\sin x$ and the $\mathrm{X}$-axis between $\mathrm{x}=0$ and $\mathrm{x}=\pi$ is

Question

Aicharya · Accepted Answer

We have to find the area bounded by $y-1=\cos x, y$ $=\sin x$ and $x$-axis betweein $x=0$ and $x=\pi$. Let us draw the above region

The area of bounded region $=\operatorname{Area}(O A C)+\operatorname{Area}(A C D)$ $\begin{aligned} & =\int_0^{\pi / 2} \sin x d x+\int_{\pi / 2}^\pi(\cos x+1) d x \\ & =[-\cos x]_0^{\pi / 2}+[\sin x+x]_{\pi / 2}^\pi \\ & =[-0+1]+\left[0+\pi-1-\frac{\pi}{2}\right] \\ & =1+\pi-1-\frac{\pi}{2}=\frac{\pi}{2}\end{aligned}$

The area bounded by the curves $y-1=\cos x, y=\sin x$ and the $\mathrm{X}$-axis between $\mathrm{x}=0$ and…

Solution