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# Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves.$y = x \ln (x + 1)$ , $y = 3x - x^2$

## Area of the region bounded between the curves is$\approx 3.191-1.498=1.693$

#### Topics

Integration Techniques

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##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

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### Video Transcript

problem is, use a graph find approximate its coordinates off the points of intersection with given curves, then find the area of the region bonding. But, pierce, you're a wise. They go to x times our X plus one. Why's because three acts minus X squared I knew things graphing wise we can find Graff is as follows. So why one this wise towns out, Max, cross one on Drew on this. Why is he reacts? Minus x squared? We have seen that intersection points are zero on DH one point nine to fix. So I guess they call you. Zero is you put one on nine. You six then and we can't see between these two points. The blue here has as a ton of it's the right one. So we have every Bonny at is two cares if he caught you into profound way too. Reacts minus exploiter minus X towns out X plus one Jax. So this is They caught you three over to X squared. Minus one half like my third ex chief Reese Power from a B minus, the integral from a bee X. I'm Sal. I won. Yes. Yeah, but then we compute the integral of X taps out on DH X plus long yaks. I see. We can use integration. My parts first we cannot. Why is there caught you X plus y use substitution then we have. This is the cultural control of why minus one. And how lax on why you want. Then I can use new substitution like you is cultural one. Why? And we promise they goto. Why one then you promise one over why And is he my half lie Squires on miles? Why, then this integral as the cultural new Temps? We So this this one? Why, squire minus y Sam's out. And why, minus the integral of your prom time? Sweetie, this is one half. Why? Minus one you want This is the one half lie squadron once. Why, you know, and why? Minus this is one horse lies squire minus why? And thus caused the numbers. See, now on the way. Convert. Why? Back to your ax? This's one, huh? X plus one squire minus X plus one damn spell in X plus one minus my force X plus one squire minus X plus one. And for our problem into Gerald's. Definitely integral from a to B of this valuable services from age being. Then this is a call. Choose this one and from a to B. Now, by using a calculator we can find while you have, this one is out one point six nine to six.

WZ

#### Topics

Integration Techniques

##### Catherine R.

Missouri State University

##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

Join Bootcamp