The value of $\mathop \smallint \nolimits_0^\infty \,\,\frac{{dx}}{{\left( {{a^2} + {x^2}} \right)}}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

The value of

\int \nolimits_0^\infty \,\,\frac{{dx}}{{\left( {{a^2} + {x^2}} \right)}}

is equal to

View answer and explanation

Correct option: B

\frac{\pi }{{2\,a}}

Option B (

\frac{\pi }{{2\\,a}}

) is correct because the integral evaluates to (1/a)arctan(x/a) from 0 to infinity, which simplifies to pi/(2a).

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