maverik877
New member
- Joined
- Jul 10, 2011
- Messages
- 2
Hello Everyone, hope you're having a great weekend.
I am having a really tough time with these volumes and solid revolutions. I cannot visualize what's happening. I tried the following problem on my own several times and I'm not sure if it's right. If someone could give me a hint or tell me if its correct, I would greatly appreciate it.
Find the volume of the solid obtained by rotating the region bounded by the given curves around the specified axis.
(a) y = x^(2) +1, y = 9-x^(2); about y = -1.
So I tried the washer method, and this is what I ended up with.
pi * integrating from -2 to 2, ((x^(2)+1)-(-1))^(2) - (9-x^(2)-(-1))^(2). simplifying this I got 24x^(2) - 96, integrating, I ended up with 8x^(3)-96x, and going from -2 to 2, I got
-128-128 = -256*pi as a final answer. I think this is probably wrong. I'm just so confused at this point, I just need some advice from people who have done this before.
Also, there is another problem of, y = e^(-x^(2)), y = 0, x = 0, and x = 1, which if I use shells for hopefully it will work.
Again, ANY help for this would be greatly appreciated.
I am having a really tough time with these volumes and solid revolutions. I cannot visualize what's happening. I tried the following problem on my own several times and I'm not sure if it's right. If someone could give me a hint or tell me if its correct, I would greatly appreciate it.
Find the volume of the solid obtained by rotating the region bounded by the given curves around the specified axis.
(a) y = x^(2) +1, y = 9-x^(2); about y = -1.
So I tried the washer method, and this is what I ended up with.
pi * integrating from -2 to 2, ((x^(2)+1)-(-1))^(2) - (9-x^(2)-(-1))^(2). simplifying this I got 24x^(2) - 96, integrating, I ended up with 8x^(3)-96x, and going from -2 to 2, I got
-128-128 = -256*pi as a final answer. I think this is probably wrong. I'm just so confused at this point, I just need some advice from people who have done this before.
Also, there is another problem of, y = e^(-x^(2)), y = 0, x = 0, and x = 1, which if I use shells for hopefully it will work.
Again, ANY help for this would be greatly appreciated.
