Mathematics

Evaluate $$\displaystyle\int_{-\pi/4}^{\pi/4}|\sin x|\ dx$$


SOLUTION
Now,

$$\displaystyle\int_{-\pi/4}^{\pi/4}|\sin x|\ dx$$

$$=2\displaystyle\int_{0}^{\pi/4}\sin x\ dx$$ [ Since $$|\sin x|$$ is an even function]

$$=2[-\cos x]_{0}^{\dfrac{\pi}{4}}$$

$$=2\left[1-\dfrac{1}{\sqrt2}\right]$$

$$=2-\sqrt2$$.
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Subjective Medium Published on 17th 09, 2020
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