# Find the exact value of Integral from 0 to infinity of x * f(x) dx?

Find the exact (not calculator) value of Integral from 0 to infinity of x * f(x) dx, given the fact that Integral from 0 to infinity of e^(-x^2) dx = sqrt(pi)/2

f(x) = xe^(-x^2)

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- rotchmLv 72 months ago
∫ x * f(x) = ∫ x * xe^(-x²) = ∫ x²e^(-x²)

Now hint: Do this by parts. What do you get?

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