The value of the integral $\mathop \smallint \nolimits_a^b \,\,\frac{{\sqrt x \,dx}}{{\sqrt x + \sqrt {a + b - x.} }}\,\,{\rm{is}}$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of the integral

\int \nolimits_a^b \,\,\frac{{\sqrt x \,dx}}{{\sqrt x + \sqrt {a + b - x.} }}\,\,\mathrm{is}

View answer and explanation

Correct option: B

\frac{1}{2}\,\,\left( {b - a} \right)

Option B (

\frac{{1}}{{2}}\,\left( {b - a} \right)

) is correct because it is derived by using the property of definite integrals where

\int \limits_a^b f(x) dx = \int \limits_a^b f(a+b-x) dx

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