I. Use the shell method to find the volume of the solid...

Transcript

00:01 If we look closely at y equals x squared, you know, look something like this.

00:06 And then the other function, i'm going to try and sneak it in kind of like this.

00:10 So i'm writing it in red because they actually meet for x minus x squared.

00:19 Because i've worked through this problem already.

00:21 They meet at the line x equals 2 that we're revolving around.

00:26 And you can double check that that's where they meet because you can set them equal to each other.

00:32 Equals x squared and i would actually add the x squared to the right side so it would be 2x squared minus 4x and then factor out a 2x out of that piece and you can see that they intersect each other if you use the zero product property at zero or two so as i go to this problem we have 2 pi the integral from 0 to 2 now you have to be careful because the radius on this problem i'll use green again, is if you look at any one of these pieces, the radius is represented by the axis of you're rotating around minus x.

01:12 That's the length of each radius in this problem.

01:16 And then the height of each cylinder, so think about if i'm revolving, that's a terrible looking.

01:21 I am not an artist, though i apologize.

01:24 If we made a cylinder and do the lateral area, the height is represented by that upper function of 4x minus x squared.

01:34 And you have to subtract off the lower function, which i have as x squared...

Question

i. Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves $y = x + 2$ and $y = x^2$ about the line $y = 4$.

Question

i. Use the shell method to find the volume of the solid generated by revolving the regions bounded by the curves $y = x + 2$ and $y = x^2$ about the line $y = 4$.

Please give Ace some feedback