The integral of x^2e^(-x^2) from -∞ to +∞ can be evaluated using the known result that the integral of e^(-x^2) over the same limits equals sqrt(π). By applying integration by parts with u = x and dv = xe^(-x^2)dx, the correct evaluation yields the result of sqrt(π)/2. This method clarifies the steps necessary to arrive at the solution, correcting previous miscalculations involving indefinite integrals.
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spaniks said:Homework Statement
Use the fact that the integral evaluated from -∞ to +∞ of e^(-x^2) is sqrt(∏) to evaluate the integral from -∞ to +∞ of x^2(e^(-x^2)).
Homework Equations
The Attempt at a Solution
I tried using integration by parts and I came down to an indefinite integral of sqrt(∏)*x^2. I know the answer is sqrt(∏)/2 but I don't see how. Can someone tell me what I am doing wrong please.