Mathematics

# Evaluate :$\int { \left( 1-x \right) \sqrt { x } } dx$

##### SOLUTION
$I=\displaystyle\int{\sqrt{x}dx}-\displaystyle\int{x\sqrt{x}dx}$

$=\displaystyle\int{{x}^{\frac{1}{2}}dx}-\displaystyle\int{{x}^{1+\frac{1}{2}}dx}$

$=\displaystyle\int{{x}^{\frac{1}{2}}dx}-\displaystyle\int{{x}^{\frac{3}{2}}dx}$

$=\dfrac{{x}^{\frac{1}{2}+1}}{\dfrac{1}{2}+1}-\dfrac{{x}^{\frac{3}{2}+1}}{\dfrac{3}{2}+1}$

$=\dfrac{2x\sqrt{x}}{3}-\dfrac{2{x}^{2}\sqrt{x}}{5}+c$

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

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