Solution 17170: Finding the Area Between Curves on the TI-83 Plus Family of Graphing Calculators.
How do I find the area between curves on the TI-83 Plus family of graphing calculators?
To find the area between curves please see the below example:
Example: Find the area of the region bounded by:
f(x)=300x/(x2 + 625)
g(x)=3cos(.1x)
x=75
1) Press [WINDOW] and set the values as below:
2) Press [Y=] and make sure that no stat plots are highlighted.
3) Enter 300x/(x^2+625) in y1.
4) Enter 3cos(.1x) in y2.
5) Press [2nd] then [Trace] [5] to select 5:intersect.
6) Press [ENTER] for the first curve and [ENTER] for the second curve. To guess, move the cursor on the intersection of the graph on the left (The value of z at the intersection which is the lower limit of the integral is stored in Ans and X).
7) Press [2nd] then [Mode] to quit to the home screen. Next press [2nd] then [pgrm] [7] and use Shade( to see the area graphically.
8) Press [VARS] then [→] to select Y-VARS.
9) Press [1] to select 1:Function then press [2] to select 2: Y2.
10) Press [,] then [VARS] [→] to select Y-VARS. Press [1] to select 1: Function then [1] to select 1: Y1.
11)Press [,] [2nd] [ (-) ] [,] [7] [5] [ ) ] [ENTER] (The screen should show Shade(Y2,Y1, Ans, 75) The graph will look like the following:
12) Press [2nd] then [Mode] to return to the home screen. Enter the expression to evaluate the integral for the shaded region using the VAR menu and Ans as above.
13) Press [MATH] [9] for fnInt(
14) Press [VARS] [→] to select Y-VARS. Press [1] to select 1: Function then [1] to select 1: Y1.
15) Press [-] then [VARS] [→] to select Y-VARS. Press [1] to select 1:Function then press [2] to select 2: Y2.
16) Press [,] [X,T,θ,n] [,] [2nd] [ (-) ] [,] [7] [5] [ ) ] [Enter]
The area is 325.84.
Please see the TI-83 Plus Family guidebooks for additional information.
Last updated: 10/15/2024