- #1
Panphobia
- 435
- 13
Homework Statement
Calculate the volume obtained by rotating the triangle bounded by y = 0, y = x, and y = 2 - x, about the line x = -2. You may use either horizontal or vertical rectangles.
The Attempt at a Solution
So since this is a triangle, I tried to split up the volume down to two integrals, one from 0 - 1, and the other from 1-2. I used vertical rectangles by the way. So I set up my first integral as
[itex]2 \cdot \pi \int_{0}^{1} (x+2)(x) \,dx[/itex]
since the shell radius would be a distance x + another 2, and then the shell height would be the x.
My second integral is
[itex]2 \cdot \pi \int_{1}^{2} (x+2)(2-x) \,dx[/itex]
then I added these together, but I did not get the correct answer, could anyone show me what the error in my steps are?