- #1
adelaide87
- 24
- 0
Homework Statement
Hi
I am trying to find the volume of a shape.I don't need help to solve, but I would like a hand setting these integrals up. I've only recently started doing volumes, so bear with me.
Using the curves:
y=x
x=2-y^2
y=0
Indicate the method used and set the integrals up (dont have to integrate) that give the volume of the solid by rotating the region around:
a) the x axis
b) the y axis
c) the line x=-2
d) the line y=1
The Attempt at a Solution
a) Use the DISK method, Integrate from 0 > 2
(pi)(y^2) dx
= (pi)(x-sqrt(2-x))^2 dx
b) Use SHELL method from 0 > 2
2(pi)(x)(y)
= 2(pi)(x)(x-sqrt(2-x))
c) and d)
Not totally sure, would I just have to incorporate that line into the formula? That is confusing me.
If someone could let me know if a and b are right, and give some guidance in c and d that would be great.
Thanks