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Use a graphing utility, where helpful, to find the area of the region enclosed by the curves.$$y=x e^{x^{2}}, y=2|x|$$

$$=0.193147$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 6

APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING

Section 1

Area Between Two Curves

Integrals

Integration

Applications of Integration

Area Between Curves

Volume

Arc Length and Surface Area

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eso. Since you're allowed to use a graphing calculator, I would just go ahead and use a graphing calculator. You can see the exit of the X squared function is the blue curve in the absolute values of V shaped green curve eso as faras finding the area between the curves. You just go to your integral, um, between zero. You can tell that they cross at zero, and this is actually should be exactly if you set them equal to each other of 56 Um, 56 If you don't believe me, I'll just give you 56.833 Um, and maybe it's not exactly 56 million. I should just write out 560.833 ankle getting answer. That's close up anyway. Um, and so then the upper function is the absolute value, But I'm just going to rank two X. You can leave it as the absolute value. This country let you do that. But that's the positive version, so we don't need to do the absolute value minus this function, which I'm just going to copy and paste. It's actually helpful to put in parentheses. I don't know if you actually need parentheses and then helicopter to do D X. Now this just looks like mumbo jumbo decimals. But looking at it, if you actually did you substitution for the Annan drift of these plugged it in, you would see that the exact answer is natural. August 2, um, minus one half. Um oh, it's a little bit off. So may a better answer was using 56 year, as I mentioned earlier. Quick, and see if I get the No, no one still off just a little bit. Um, but the important thing is finding these values and understanding how to get there. Um, so far, you out just around my answer to be 0.193 instead of the exactly into that the book says.

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