Mathematics

# Evaluate the following integral:$\displaystyle\int_{0}^{\pi}\cos^{2}x\ dx$

##### SOLUTION
Given $\displaystyle\int_{0}^{\pi}\cos^{2}x\ dx$

$=\displaystyle \int _0^{\pi} \dfrac {1+\cos x}{2} dx$   [$\because \cos^2 x=\dfrac {1+\cos 2x}{2}$]

$= \displaystyle \int _0^{\pi} \left(\dfrac 12+\dfrac 12 \cos x \right)dx$

$=\left.\dfrac x2+\dfrac {\sin x}{2}\right]_0^{\pi}$ .

$=\dfrac \pi 2$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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