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)
Respond to this Question
Similar Questions

Calculus
Solve these indefinite and definite integrals. [integration sign] 4j5j^3 dj I got 2j^2  5/4j^4... is this my final answer? 
Calculus
I'm doing statistics homework and am stuck on a problem using integration. The problem gives a distribution where for x>1, f(x) = k x^6. I am then asked to "Determine the value of k for which f(x) is a legitimate pdf. " To be a … 
calculus
Calculate definite integral of dx/(x^4 * sqrt(x^2 + 3)) Over (1,3) I start with the substitution x = sqrt(3)*tan t so: sqrt(x^2 + 3) = sqrt(3) * sec t dx = sqrt(3) * sec^2 t dt x^4 = 9 * tan^4 t The integral simplifies to: = dt/(tan^3 … 
calculus
what is the answer for the integral of (1/(xln(x)) from 1 to infinity? 
calculus
how do you determine the convergence of : definite integral from 1> infinity of lnx/(x^3)? 
Calculus
Evaluate the definite integral from [0,4] 4x^2 dx, by using its definition as a limit of approximating sums. First, I solve analytically so I know the answer I am trying to reach: 4/3 * x^3 over [0,4] = 4/3 * 4^3 = 256/3 Now, by approximating … 
MATH
I have been trying to do this problem for a couple of days but i cant seem to get the answer. Any help would be greatly appreciated. For each of the following forms determine whether the following limit type is indeterminate, always … 
calculus
find the definite integral that is equivalent to lim n>infinity of sum over i=(1,n) n/(n^2+i^2) since definite integral of f(x) dx over (a,b) = lim n>infinity sum over i=(1,n) f(a + (ba)i/n) * (ba)/n then: f(a + (ba)i/n) … 
Calculus
I've been trying to solve the improper integral of ln(x)/sqrt(x) dx as a=1 and b=infinity I am required to solve for this question and according to my answer, it is divergent. However, my answer is infinity4. Is it acceptable to say … 
calculus (please with steps and explanations)
consider the function f that is continuous on the interval [5,5] and for which the definite integral 0(bottom of integral sign) to 5(top of integral sign) of f(x)dx=4. Use the properties of the definite integral to evaluate each integral: …