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# Determine whether each integral is convergent or divergent. Evaluate those that are convergent.$\displaystyle \int_{-\infty}^\infty xe^{-x^2}\ dx$

## The integral converges to 0

#### Topics

Integration Techniques

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##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

for this integral we can right on us. Negative. Infinity to zero off a function next to Pam's. Eat too negative. X square. Yeah, thanks. Us zero to infinity ofthe dysfunctional X times each native square The ex No, we computed the first. Integral. This is Echo Two. It is one. This is Nico Tio Lim. It goes to make TV impunity of the integral A zero x Temps Deacon. Native Max. Where? Yes, wait. Andi were computed definitely integral first and this fire. But this part this is Echo two. Yeah. We use use of substitution that you coached. You explain. Then this is ICO Tio. You need to make the view. Japan's one half do you? No, from a square to zero. And this is Echo two. One half hands make active eat Connected you from a square, you zero by computation. This's Iko too. Make active. One half cam's one minus you too Negative a square. And this is dysfunction goes to I mean, if you want half what a goes to make Jimmy affinity. So the first part is he going to make you one half similarly waken compared to the second mark and the second part it. Zico, too, want half. His answer is equal to zero. So this function, integral with this function is converted and the answer is zero.

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#### Topics

Integration Techniques

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp