### Home > APCALC > Chapter 8 > Lesson 8.1.3 > Problem8-29

8-29.

Set up and evaluate an integral to calculate the area enclosed in the ellipse $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$. Homework Help ✎

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

Solve for $y$. This will be the integrand. Note: Because of symmetry across BOTH the $x$- and $y$-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.