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Use a CAS to find the exact area enclosed by the curves$y=x^{5}-2 x^{3}-3 x$ and $y=x^{3}$.

$$14.770$$

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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uh, So I went ahead and ah, typed in the graph. The equations of these graphs that doing is a little bit more, um, agency that X cubed is in red. The extra 50 IAEA is in blue, and what's important is finding the points of intersection that are outside of on the furthest. Now they do intersect at X equals zero. But you can actually ignore that in this problem. Make sure I don't think the Intersect again. Doesn't look like it. Okay, so I really can't negative X equals name 1.947 in positive 1.9477 So starting new equation hit functions miscellaneous right here. Negative 1.947 to possible in 0.9 course of it now because I'm doing the problem this way. You want to hit the absolute value again that's under functions, Um, or no, it's not. It's right here. But I actually used a calculator shortcut. And what you can do is it doesn't matter which function you take. Um, actually, let me take this Alice to the top. Because if you do the top one, there's one more stuff you have to dio minus in Corinth theses because you want to make sure you subtract of everyone in these pieces. Um, I'm hitting command. See, by the way, I'm copying and pasting that right here. And you also just say the X now by doing the absolute value what it does, it is. It always takes, um, the positive version of these answers. So if you look, these two areas would cancel each other out. If I drop the absolute value and just delete those absolute values your quick and notice you get an answer. Uh, ups you get an answer zero because they cancel each other out. So that's why you need tohave the absolute value in there so that they don't cancel each other out. So about 14.770 if you around a three decimal places, um, and other graphing calculators would give you the perfect answer. This one does not like a fractional answer. This one just gives you a decimal. I don't know how to fix that.

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