Mathematics

Evaluate the following definite integral:

$$\displaystyle\int_{0}^{\pi/2} \sin x \cos x\ dx$$ 


SOLUTION

Consider, $$I=\displaystyle\int_{0}^{\pi/2} \sin x \cos x\ dx$$ 

Let $$t=\sin x \implies dt=\cos x dx $$

$$x \to 0 \to \pi/2$$ and $$t \to 0 \to 1$$ 

$$I=\displaystyle \int _0^1 t \ dt $$ 

$$I= \left[\dfrac {t^2}2 \right] _0^1 =\dfrac 12$$

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Subjective Medium Published on 17th 09, 2020
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