(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Set up the double integral in rectangular coordinates for calculating the volume.

The solid is created by the equation

2. Relevant equations

Fubini's Thereom ∫_{R}∫f(x,y)dA = ∫_{a}^{b}∫f(x,y)dydx

3. The attempt at a solution

The shape created by Z = 30 - x^{2}- y^{2}is 3d parabola facing downards.

Since it is bounded by Z = 5, the base shape is a circle at origin with radius 5 since

5 = 30 - x^{2}- y^{2}is equal to x^{2}+ y^{2 }= 25

As a result x is bounded by -5 and 5 while y is bounded by -√(25-x^2) and √(25-x^2)

As a result to set up the double integral

∫_{-5}^{5}∫_{√(25-x^2)}^{√(25-x^2)}30-x^{^2}-y^{^2}dydx

Are the integral boundaries in correct?

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# Homework Help: Setting up Double Intergrals to Calculate Volume

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