- #1
qq545282501
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Homework Statement
use a double integral to find the volume bounded by the paraboloid :[tex]z=4-x^2-y^2[/tex], xy-plane and inside a cylinder: [tex]x^2+y^2=1[/tex]
Homework Equations
x=rcosθ y=rsinθ
The Attempt at a Solution
the radius of the area of integration is 1, since its determined by the cylinder only, and the cylinder has radius of 1.
the cylinder has an infinite z value, so Z is like like [tex]4-r^2- 0[/tex]
so I got this:
[tex] \int_{θ=0}^{2π} \int_{r=0}^1 (4-r^2)r \, dr \, dθ[/tex]