Mathematics

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


SOLUTION

Given $$\displaystyle \int _0^{\pi/2} \sin x \cos x dx $$

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

$$x\to 0\to \dfrac \pi 2 $$

$$t\to 0\to 1$$

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

$$=\left.\dfrac {t^2}2\right|^1_0$$  [$$\because\int x^n=\dfrac{x^{n+1}}{n+1}$$]

$$=\dfrac 12-0$$

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