Let I=∫ _ 0 ^π #160; / 2 #160; sin #160; xdx #160; = [ cos #160; x ] _ 0 ^π #160; / 2 #160; = [ cos #160; π #160; / 2 co ...

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Integration of Piecewise Continuous Functions

∫ 0π/2sin xdx

Question

$\int_{0}^{\frac{π}{2}} sin x d x$

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Solution

Let $\begin{matrix} I = \int_{0}^{\frac{π}{2}} sin x d x = - {[cos x]}_{0}^{\frac{π}{2}} = - [cos \frac{π}{2} - cos 0] = - [0 - 1] = 1 \end{matrix}$
Hence $1$ is the required answer.

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