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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]