CPM Homework Help : APCALC Problem 8-29

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

Step 1:

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

Step 2:

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.

Answer:

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