Mathematics

# Solve:$\displaystyle \int_0^{\pi/2}sinx \cos^3 xdx$

##### SOLUTION
$\int _{ 0 }^{ \dfrac { \pi }{ 2 } }{ \sin x{ \cos }^{ 3 }xdx } \\ Let\quad \cos x=t\\ \Rightarrow \sin xdx=-dt\\ also,\quad at\quad x=0;t=1\\ and\quad at\quad x=\dfrac { \pi }{ 2 } ;t=0\\ \therefore \int _{ 0 }^{ \dfrac { \pi }{ 2 } }{ \sin x{ \cos }^{ 3 }xdx } =-\int _{ 1 }^{ 0 }{ { t }^{ 3 }dt } \\ ={ -\left[ \dfrac { { t }^{ 4 } }{ 4 } \right] }_{ 1 }^{ 0 }\\ =\dfrac { 1 }{ 4 }$

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