Solution 11753: Finding the Area Between Two Curves on the TI-89 Family, TI-92 Plus, and Voyage™ 200.
How do I find the area of the region shared by two functions between their intersecting points on the TI-89 Family, TI-92 Plus, and Voyage 200?The following example shows how to find the area between two curves:
Example: Find the area between the curves y=x^2+x-15 y=2x-3.
• Press the [◆][F1]
• Enter y1=x^2+x-15 and y2=2x-3
• Press [◆][F3] to graph both functions.
• Press [F5] and choose 5:Intersection.
• Follow the prompts from here.
• Press [ENTER] twice to select the two curves.
• The lower bound is any point to the left of the intersection on the x axis.
Use the left and right arrow keys to move the cursor, and Press [ENTER] to place the bound.
• The upper bound is any point to the right of the intersection on the x axis. Use the left and right arrow keys to move the cursor, and press [ENTER] to place the bound.
• After pressing [ENTER], the intersection coordinates will display.
• Repeat this procedure for both intersections and copy down the points on a scratch sheet of paper.
For this example, the intersection points will come out to be (-3,-9) and (4,5).
• Press [HOME] to go to the Home screen.
• Press [CLEAR] to clear the entry line, if necessary.
• Press [2nd] [MATH]   to insert the abs( command.
• Press [F3] [ALPHA] [B] to insert the nInt( command.
• Input y1(x)-y2(x),x, -3, 4)).
• Press [ENTER]. The calculator will display 57.1667.
Please see the TI-89 family, TI-92 family, and Voyage 200 guidebooks for additional information.