Calc 3.
Set up, but do not evaluate, an iterated integral for the volume of the solid.
Under the graph of f(x,y)=25-x^2-y^2 and above the xy-plane.

I think the outer integral is 0 to 5, but I'm stuck on the inner integral because I can get it to depend on two variables, but not 1.

Question

Calc 3.
Set up, but do not evaluate, an iterated integral for the volume of the solid.
Under the graph of f(x,y)=25-x^2-y^2 and above the xy-plane.

I think the outer integral is 0 to 5, but I'm stuck on the inner integral because I can get it to depend on two variables, but not 1.

anonymous · Answer

Evaluate 5 and 3.14 pie and subtract. That and multiply!

tkhunny · Answer

In the x-y plane, z = 0, giving the circle x^2 + y^2 = 25.
This is wonderfully symmetric, so work in just the first octant:

$4\cdot\int\limits_{0}^{??}\int\limits_{0}^{??} 25 - x^2 - y^2 \;dx\;dy$