Mathematics

Evaluate:
$$\displaystyle \int_{\theta =0}^{\pi}\sin \theta . d\theta$$


SOLUTION
$$\displaystyle\int_{0}^{\pi}{\sin{\theta}d\theta}$$
Let $$t=\cos{\theta}\Rightarrow dt=-\sin{\theta}d\theta$$
When $$\theta=0\Rightarrow t=\cos{0}=1$$
When $$\theta=\pi\Rightarrow t=\cos{\pi}=-1$$
$$\displaystyle\int_{0}^{\pi}{\sin{\theta}d\theta}$$
$$=\displaystyle\int_{1}^{-1}{-dt}$$
$$=-\left[t\right]_{-1}^{1}$$
$$=-\left[1+1\right]$$
$$=-2$$
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Subjective Medium Published on 17th 09, 2020
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