Finding volume using triple integral

woogirl14
Messages
2
Reaction score
0
1. Homework Statement

I need to find the volume of a solid formed by the following equations:
x^2+y^2 > 1
x^2+z^2 = 1
z^2 + y^2 =1


3. The Attempt at a Solution

I know that it is a triple integral and the integrand is 1.
I also know that I need to use dzrdrd\theta.
 
Physics news on Phys.org
i think u mean dxdydz

u need to first evaluate the h(x,y) = \int dz f(x,y,z)

between the limits on z (which may depend on x and y ).
2. Evaluate the function g(x) given by
g(x) = \intdyh(x, y),
between the limits on y (which may depend on x ).
3. Finally integrate g(x) over x between the limits on x.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top