Mathematics

# $\int_{0}^{a}\dfrac{\sqrt{x}}{\sqrt{x}+\sqrt{a-x}}dx$

##### SOLUTION
We have,
$I=\int _{ 0 }^{ a }{ \dfrac { { \sqrt { x } } }{ { \sqrt { x } +\sqrt { a-x } } } dx }$ $........(1)$

Apply property,
$\\ I=\int _{ 0 }^{ a }{ \dfrac { { \sqrt { a-x } dx } }{ { \sqrt { x } +\sqrt { a-x } } } }$   $........(2)$

On adding equation (1) and (2), we get
$\\ 2I=\int _{ 0 }^{ a }{ dx }=a \\ I=\dfrac { a }{ 2 }$

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

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