Mathematics

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

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

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

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

$t\to 0\to 1$

$\implies \displaystyle \int _0^{1} t dt$

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

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

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

#### Realted Questions

Q1 Subjective Medium
Solve $\displaystyle \int\limits_{\pi /6}^{\pi /3} {\frac{1}{{\sin 2x}}} \,dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle\overset{\pi/2}{\underset{0}{\displaystyle\int}}\cos^3xdx =$ ___________.
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Q3 Single Correct Hard
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Prove that $\displaystyle\int_0^{\pi/2}$ $ln(\sin x)dx=\displaystyle\int_0^{\pi/2}ln(cos x)dx=\int_0^{\pi/2}\,\,ln(sin2x)dx=-\dfrac{\pi}{2}.ln 2$.