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
$$\\ 2I=\int  _{ 0 }^{ a }{ dx }=a \\ I=\dfrac { a }{ 2 } $$

Hence, this is the answer.
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Subjective Medium Published on 17th 09, 2020
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