Mathematics

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

$\dfrac 1 2$

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

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

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

$t\to 0\to 1$

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

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

$\Rightarrow\dfrac 12-0=\dfrac 12$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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