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Evaluate the integral, given that$\int_{0}^{\infty} e^{-x^{2}} d x=\frac{1}{2} \sqrt{\pi}$$\int_{0}^{\infty} x^{2} e^{-x^{2}} d x$

$\frac{\sqrt{\pi}}{4}$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 8

Improper Integrals

Integration Techniques

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Okay, so we use you Devi on VD you to value with this. We end up with X times e to the power of negative X squared divided. But to evaluate this from zero up to in any way plus the integral from zero to infinity off 1/2 eaten the power of negative X squared X Evaluating this one's yours if any reason. Enough with zero plus 1/2 time leading to go from zero to infinity and eat the power of negative X X squared. Yes, Thanks. Squared yes to this is equal to 1/2 times of 1/2 times square Too high, which is the square root of pi over four. And, uh, yeah, so were given. We got that this legal disqualified because we're given that the integral from zero to infinity and eat the powerful negative X squared accident 1/2 times the square root of pi

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