A. Set up an integral for the area of the surface generated...

a. Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis. b. Graph the curve. c. Use technology to find the surface area numerically. xy = 2, 4 ? y ? 6; y-axis a. Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) A. $S = \int_{4}^{6} \sqrt{\Box} dy$ B. $S = \int_{4}^{6} \sqrt{\Box} dx$ b. Choose the correct answer below. c. The area of the surface is square units. (Do not round until the final answer. Then round to the nearest hundredth as needed.)

Transcript

0:00 I'm graphing first.

00:01 So i'm going to do part b.

00:03 So when i see taking this function, y equals, well, i know it says x, y equals 5, and i like to write things as functions would be y equals 5 divided by x.

00:20 And the way that would be written or graph to be something like this.

00:24 And you can pick out some key points like when x equals 1, you would get 5 for y, or you can have if you know x equals 5 then y would equal 1 but we actually don't even care about that we have the values between 2 and 8 so that's y equals 2 and then y equals 8 would be up here and we're revolving around the y axis so basically we have these disks in here i don't know if they want you to show those disks but basically the graph would look something like this.

01:06 So there's part b.

01:08 So how would you set up this integral? well, first of all, you should have actually solved this problem for x.

01:18 Because it's the disk method, where you're just finding the area of all those circles and the area form is pi r squared.

01:27 And so if you're doing this properly, the s is the integral from 2 to 8.

01:36 And this pie is a constant, so just write that down.

01:39 And then the function is...

01:41 Oops, i wrote the wrong thing down.

01:45 Ah, i thought i hit the racer.

01:48 There we go.

01:51 5 over y.

01:53 That thing is being squared.

01:55 D -y.

01:56 Now, at this point, it would be up to you.

01:59 How you would.....

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