1.

`int_(a)^(b)(sqrt(x))/(sqrt(x)+sqrt(a)+b-x) =dx=......`A. `a+b`B. `(b-a)/(2)`C. `a-b`D. `(a-b)/(2)`

Answer» Correct Answer - B
Let `I = int_(a)^(b) (sqrt(x))/(sqrt(x) + sqrt(a + b - x)) dx`
`= int_(a)^(b) (sqrt(a + b - x))/(sqrt(a + b - x) + sqrt(a + b - (a + b - x)))`
`I = int_(a)^(b) (sqrt(a + b - x))/(sqrt(a + b - x) + sqrt(x))`
On adding Eqs. (i) and (ii), we get
`2I = int_(a)^(b) (sqrt(x) + sqrt(a + b - x))/(sqrt(x) + sqrt(a + b + x)) dx`
`implies 2I = int_(a)^(b) dx = (x)_(a)^(b) = b - a`
`implies I = (b - a)/(2)`


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