calculus
posted by mathstudent .
Assuming that:
Definite Integral of e^(x^2) dx over [0,infinity] = sqrt(pi)/2
Solve for
Definite Integral of e^(ax^2) dx over [infinity,infinity]
I don't know how to approach the new "a" term. I can't use usubstitution, integration by parts, partial fractions, or trig substitution. How do I do this?

Substitute x = t/sqrt(a). The integral then becomes:
a^(1/2)Integral of e^(t^2) dt over [infinity,infinity] =
2 a^(1/2)Integral of e^(t^2) dt over [0,infinity] = sqrt(pi/a)