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GogumaDork

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## Homework Statement

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

The solid is created by the equation

## Homework Equations

Fubini's Thereom ∫

_{R}∫f(x,y)dA = ∫

_{a}

^{b}∫f(x,y)dydx

## 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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