Evaluate the improper integral int_{0}^{infty} x e^{-x^{2}} d x

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Accepted Answer

Step:1 ：Given the improper integral (int_{0}^{infty} x e^{-x^{2}} d x)Step:2 ：We can use the method of integration by substitution. Let&#x27;s set (u = x^2), then (du = 2x dx)Step:3 ：Rewrite the integral in terms of (u) and solve itStep:4 ：The integral has been evaluated successfully. The result is (sqrt{pi}/4)Step:5 ：Final Answer: (boxed{frac{sqrt{pi}}{4}})

Answer

Step: 1 ：Given the improper integral (int_{0}^{infty} x e^{-x^{2}} d x)Step: 2 ：We can use the method of integration by substitution. Let&#x27;s set (u = x^2), then (du = 2x dx)Step: 3 ：Rewrite the integral in terms of (u) and solve itStep: 4 ：The integral has been evaluated successfully. The result is (sqrt{pi}/4)Step: 5 ：Final Answer: (boxed{frac{sqrt{pi}}{4}})

Evaluate the improper integral $\int_{0}^{\infty} x e^{- x^{2}} d x$

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Evaluate the improper integral $\int_{0}^{\infty} x e^{- x^{2}} d x$