If $\mathop \smallint \limits_0^\infty \,{e^{ - {x^2}}}\,\,dx = \sqrt {\frac{\pi }{2}} $ then $\mathop \smallint \limits_0^\infty \,\,{e^{ - a{x^2}}}\,\,dx,\,\,\;a > 0$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \limits_0^\infty \,{e^{ - {x^2}}}\,\,dx = \sqrt {\frac{\pi }{2}}

then

\int \limits_0^\infty \,\,{e^{ - a{x^2}}}\,\,dx,\,\,\;a > 0

View answer and explanation

Correct option: D

\frac{1}{2}\,\,\frac{{\sqrt \pi }}{a}

Option D (

\frac{1}{2}\,\frac{{\sqrt {\pi } }}{a}

) is correct because it follows from a u-substitution and the given integral value.

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