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
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