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Use a graphing utility, where helpful, to find the area of the region enclosed by the curves.$$y=\frac{1}{x \sqrt{1-(\ln x)^{2}}}, y=\frac{3}{x}$$

$$=3.1949353278$$

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. I'm glad they're using a graphing calculator on this. I don't like that I have the same color. So me change colors here. Eso the blue curve is ah is drawn already on, and then the red curve. Is this three or X? Um, so what you need to do is figure out these points of intersection and I'm looking at the X values 0.39 and 2.567 So you can do the integral, which is located right here from 0.3922 point. I think I copied it down correctly. Yeah, these are just approximations, by the way. I might be a little bit off, And, uh, between those two points, um, the red curve is is larger. Um, so I'm gonna do three over x minus, and I'm just gonna copy and paste this value from now. If you're doing all of this by hand, there's going to be a lot of, um, new substitution. Let U equal natural log of X and the derivative of natural log of X is one over X, um, de X. So you can substitute. And then from there you have an inverse sine function. Um, a lot of work. Um, and then you couldn't replace this with so because we called. It's just ah, lot of work. What you'd want to this factor out of one over X in both these d X, you can place a d u. Um, so hopefully everything I said made sense. Um, but you need to go to a calculator anyway, So you might as well use the tool to its full capacity. Um, And because, um, I don't think these air exact values your find approximating to 3.195 Um, depending on where that calculator asked you to. So, um, hopefully you kind of followed along with my explanation on how to do you substitution if your teacher makes you. But since you have to use a calculator, I would just, you know, just say I used my calculator. It has been this way. Definitely need a nose knowledge to yet 1.3 air site 3.195 as your answer

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