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By using the properties of definite int...

By using the properties of definite integrals, evaluate the integrals`int_0^a(sqrt(x))/(sqrt(x)+sqrt(a-x))dx`

Text Solution

Verified by Experts

We have,
`I=int_0^a [sqrt(​x)]/[sqrt(x)+sqrt(a−x)]dx ........(1)​`
Apply property,
`I=int_a^b f(x)dx=int_a^b f(a+b−x)dx​`
Therefore,
`I=int_0^a sqrt(​a-x)/[sqrt(a-x)+sqrt(a-a−x)]dx `
...
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