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
Questions 203525
Subjects 9
Chapters 126
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