plz help me top solve-integrate e^-2(y)^2..limit is 0 to infinity

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plz help me top solve-integrate e^-2(y)^2..limit is 0 to infinity

Mathematics
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please write it with help of equation button
i just joined the group,donno where it is
there is a button named 'equation' just below the space to type reply

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\[\int\limits_{0}^{\infty} (e ^{-2y ^{2}})dy\]
this is the question
is it some type of error function?
yes it is
limit x approaches infinity?
yes
HINT: substitue with x = y^2, replace dy, then use 'integration by parts' the replacement for dy involves an x to the power -1/2, and the squared y terms is eliminated from the e, being replaced by -2x.
NOTE: the limits will stay the same
the answer has \[\Pi\] in the term,integration by parts wont simply solve the problem
you can solve it numerically since it is definite integral --> equals approx 0.63
i want to know is it representing any function for which there is direct answer,for example we know the results of beta function without solving it analytically
i don't think there is for this integral
this is differential calculus
answer is \[(1\div2)\sqrt{\pi/2}...anybody who knows what function properties \it used??\]
anybody who knows what function properties it used??

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