I need your help, /wsr/.

>>371356
OP here, specifically on the steps to complete the problem

You're doing shell integration. Look at a tutorial on that.

>>371362
Yeah, but that's not the problem I have.

The problem is I'm an algebra brainlet and can't figure out how to set the "y =" equation to an "x = " equation

>>371358
1.- Draw/imagine the line of the equation.
2.- Imagine that it rotates around the y axis.
3.- Now imagine the same but only care about the part that goes from x=0 to x=2.

>>371363
This doesn't matter.

>>371364
I get that, but I'm integrating with respect to y so it does matter. Also, since I'm integrating with respect to y my bounds aren't going to be from x = 0 to x = 2. it's going to be from y = 0 to y = equation.

>>371363
There's a standard equation for volume by shell revolution in y=f(x) form. If your instructor hasn't taught you that yet, it shouldn't be on the homework, but whatever.

http://www2.bc.cc.ca.us/resperic/Math6A/Lectures/ch6/2/shell.htm

This gives pretty short and simple instructions on what the formula is and why.

>>371356
you want to integrate y (x sqrt(4-x^2)) from x=0 to x=2

then you visualize what this looks like in 2d space (it looks like a line from where you integrate if you look at it from the xy plane or topdown)

to get it into a solid you would have to rotate it like a circle so you just multiple by 2pi which effectively rotates it around in a circle (it's a result of a rotationally invariant solid which you'll see in calc 3)

hopefully this helps