- #1
toothpaste666
- 516
- 20
Homework Statement
set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations
y = 4 - x^2
z= 4 - x^2
first octant
The Attempt at a Solution
I am fairly confident in my ability to evaluate double integrals , but I am having a problem figuring out how to set this one up. In the example in my book they give two equations for z and equate them to find the region in the xy plane from this region they find the limits of integration.
I think for this one I have to rewrite the first equation in terms of z?
so z = f(x,y) = y + x^2 - 4 = 0
and then I set this equal to the other equation for z
y + x^2 -4 = 4 - x^2
y -4 = 4 - 2x^2
y = -2x^2 + 8
I am not sure if anything up to here is correct and I don't know where to go from here. can someone give me a hint to help me get started ?