Mathematics

Evaluate the following definite integral:

$$\displaystyle \int _0^{\pi/2} \sin x \cos x dx $$ is equal to


SOLUTION
$$I=\displaystyle \int _0^{\pi/2} \sin x \cos x dx $$

$$\sin x=t\implies \cos x dx=dt\\x\to 0\to \dfrac \pi 2\\t\to 0\to 1$$

$$I=\displaystyle \int _0^{\pi/2} t dt$$

$$I=\left.\dfrac {t^2}2\right|^1_0$$

$$I=\dfrac 12-0$$

$$I=\dfrac 12$$  
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Subjective Medium Published on 17th 09, 2020
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