# Using geometry, evaluate the double integral. doubleintegral_D sqrt(64 - x^2 - y^2) dA over the...

## Question:

Using geometry, evaluate the double integral.

{eq}\iint_{D} \sqrt{64 - x^{2} - y^{2}}dA \text{ over the circular disk } D: x^{2} + y^{2} \leq 64 {/eq}

## Double Integrals:

In much the same way integrating the difference between two curves gives us the area between them, integrating the difference between two surfaces gives us the volume between them. When the surface is one familiar from geometry, we can use geometry to evaluate the integral.

Let' think about what the integral is describing. The top surface is

{eq}\begin{align*} z &= \sqrt(64 - x^2 - y^2) \\ z^2 &= 64 - x^2 - y^2 \\ x^2...

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