Estimate the area of the region inside the ellipse which is the graph given by the parametric equations:

**y = g(t) = 3 cos(t)**

Using JKGraph:

- Click on the
*XY*button so that it changes to*Param*. - On the
*Formulas*menu, choose*Parametric Formulas: X=F(T) & Y=G(T)*. - At the prompt
*X(T) =*, type in5*sin(t) and at the prompt*Y(T) =*, type in3*cos(t) - Move to the prompt
*T Starting Value*and enter 0. - Move to the prompt
*T Ending Value*and enter 6.28. - Click on the
*World Graph Domain*button. - Move to the prompt
*Graph X Minimum Value:*and enter -5.1. - Move to the prompt
*Graph Y Minimum Value:*and enter -5.1. - Move to the prompt
*Graph X Maximum Value:*and enter 5.1. - Move to the prompt
*Graph Y Maximum Value:*and enter 5.1. - Click on the
*OK*button. - Click on the
*Edit Integral Domain*button. - If necessary, move to the prompt
*Integral Upper Limit*and enter 6.28. - If necessary, move to the prompt
*Integral Lower Limit*and enter 0. - Choose the
*Integral Method*. - Click on the
*OK*button twice and then you will see the graph of the ellipse. - Click on the Integral button and you will see the following.
The approximate area is given at the bottom of the screen.