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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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