## anonymous 4 years ago Rotate the region bounded by the given curves about the given line and find the volume resulting solid. x=1+y^2 and the xaxis from x=1 to x=5 about y=3

1. anonymous

|dw:1328507665468:dw| we need the function in terms of x, solving for y y = sqrt(x-1) outer radius(R) = 3 inner radius(r) = 3-sqrt(x-1) $V = \pi \int\limits_{1}^{5}3^{2} -(3-\sqrt{x-1})^{2} dx$

2. anonymous

Is this using disk or shell method?

3. anonymous

disk or washer method

4. anonymous

Do you know how to do it using shell?

5. anonymous

each vertical cross-section is a ring with outer circle and inner circle

6. anonymous

i can try...i primarily use the disk method though hold on

7. anonymous

Thanks

8. anonymous

ok radius = 3-y height = 5-(y^2 +1) = 4-y^2 $V = 2\pi \int\limits_{0}^{2}(3-y)(4-y^{2}) dy$