# Math Help - Integration and volume help?

1. ## Integration and volume help?

I need some help with a volume integration problem.

I'm supposed to graph it, then find the area, and then the volume. I can get the graph, but then I get confused. Any help?

2. Originally Posted by OhhCalculus
I need some help with a volume integration problem.

I'm supposed to graph it, then find the area, and then the volume. I can get the graph, but then I get confused. Any help?
What methods are you familiar with?

3. Originally Posted by OhhCalculus
I need some help with a volume integration problem.

I'm supposed to graph it, then find the area, and then the volume. I can get the graph, but then I get confused. Any help?
area ...

$\displaystyle A = \int_0^1 \sqrt{x} - x \, dx$

volume using cylindrical shells w/r to x ...

$\displaystyle V = 2\pi \int_0^1 (2-x)(\sqrt{x} - x) \, dx$

volume using washers w/r to y ...

$\displaystyle V = \pi \int_0^1 (2-y^2)^2 - (2 - y)^2 \, dy$

4. I'm familiar with both, but for this assignment we have to use washer method. Thanks for the help. I ended up with π/5, is that remotely correct?

5. Originally Posted by OhhCalculus
I'm familiar with both, but for this assignment we have to use washer method. Thanks for the help. I ended up with π/5, is that remotely correct?
Not correct.

6. Ohh, woops. I went back through and realized I completely messed up with foiling in the beginning. I redid it and got 8π/15, is that any closer? :/

7. that's fine.