Estimate the area of the region which lies inside the loop of the graph of the curve given by the parametric equations:

y = g(t) = 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 int^2+1 and at the prompt*Y(T) =*, type int^3-t+3 - Move to the prompt
*T Starting Value*and enter -2. - Move to the prompt
*T Ending Value*and enter 2. - Click on the
*World Graph Domain*button. - Move to the prompt
*Graph X Minimum Value:*and enter 0. - Move to the prompt
*Graph Y Minimum Value:*and enter -1. - Move to the prompt
*Graph X Maximum Value:*and enter 5. - Move to the prompt
*Graph Y Maximum Value:*and enter 5. - Click on the
*OK*button. - Click on the
*Edit Integral Domain*button. - If necessary, move to the prompt
*Integral Upper Limit*and enter 1. - If necessary, move to the prompt
*Integral Lower Limit*and enter 0. - Set the
*Number of Subinterals*to be 10. - Choose the
*Integral Method*. - Click on the
*OK*button twice and then you will see the graph of the curve. - Click on the Integral button and you will see the following.
Note that the approximate area, given at the bottom of the screen, is 1.3701.

- On the
*Domains*, pick*Integral Domain*. - Move to the prompt
*Integral Upper Limit*and enter 0. - Move to the prompt
*Integral Lower Limit*and enter -1. - Click on the
*OK*button and then you will see the graph of the curve. - Click on the Integral button and you will see the following.
Note that the approximate area, given at the bottom of the screen, is -1.6616; it follows that the desired approximation of the area inside the loop is 1.6616 - 1.3701 = .2915.