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Use a graphing utility, where helpful, to find the area of the region enclosed by the curves.$$y=x^{3}-2 x^{2}, y=2 x^{2}-3 x$$

$$\frac{37}{12}$$

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

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

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In grammar, determiners ar…

02:00

Use a graphing utility, wh…

01:42

01:49

02:06

01:54

02:30

02:22

Use a double integral to c…

07:15

Sketch the region enclosed…

03:10

Graph the curves $y=x^{2}-…

06:52

Use a graph to find approx…

Uh, okay, so I really graft. I used a graphing calculator to ndgraf both functions. And what's important here is ah, where the x values were. These graphs intersect. Um, so maybe I should, uh I could show you a swell is if you create another equation. Um, so if you notice from 0 to 1 the red curve, the X cubed function is greater. Um, and then from 1 to 3, the quadratic is greater. It's above the red function. Um, but May I could point out for you is if you do the absolute value of these things and they also put in parentheses. Happy that and then subtract off with parentheses. This function, what you'll see is my new graft takes everything and puts it above the X axis. And, um, we hide that again. Um, you can actually see that the area in between these when you add them together stays positive. Um, so this might be a good visual for you to understand, as you know, to the, um, in a role which is under my function tool, Miscellaneous. Um, from where the grass would have intersected if I still had them up on the screen, but actually makes sense that they intersect because at zero in three, because that's if they intersect their equal. If you subtract them from each other, if they're equal and you subtract, you get zero for that white corner. So does actually make sense. That 0 to 3. Are you going? You reverse the video to do that, and then I could just copy that over. Um, and you can see the answer of 3.83 Um, but I believe as a fraction is 37 calls. So depending if your teacher likes decimals or fractions. Um, that's what I would do. Teoh. Get the answer. Use a calculator.

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