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8-29.

Set up and evaluate an integral to calculate the area enclosed in the ellipse . Homework Help ✎

Find the roots of the ellipse. These will help you determine the bounds of integration.

Solve for . This will be the integrand. Note: Because of symmetry across BOTH the - and -axes, you can find the area of half (or a fourth) of the ellipse, and then double (or quadruple) the result.

Use a calculator to evaluate the integral or graph the integrand and recognize its geometric shape.