Mathematics

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

$\dfrac 12$

##### SOLUTION
$I=\displaystyle \int_0^{\pi/2}\sin x\cos xdx$

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

$x\to 0\to \dfrac \pi 2\\t\to 0\to 1$

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

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

$I=\dfrac 12-0=\dfrac 12$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

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