Shade the area under a graph
Draw a curve and let the graph tools find and shade the area between it and the x-axis.
On a graphing calculator you can see the integral. Graph the function, ask for the integral, give the left and right limits, and the area is shaded as the answer appears.
Seeing the shaded region helps you check that you picked the right limits.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Press y= and type X² as Y1, then press graph to draw it.
y=X,T,θ,nx²graphOpen the CALC menu (2nd, then trace) and choose 7, the integral.
2ndCALCtrace7Type the lower limit 0 and press enter, then the upper limit 1 and press enter. The area is shaded.
0enter1enter
You should see∫f(x)dx=.3333333333
Natural Color Graphing
Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.
Open the graph screen from the main menu, type X² on the first line and press EXE.
MENU3X,θ,Tx²EXEPress F6 to draw the graph, then F5 for G-SOLV, F6 to see the next page and F3 for ∫dx.
F6F5F6F3Enter the lower limit 0 with EXE, then the upper limit 1 with EXE.
0EXE1EXE
You should see∫dx=0.3333333333
Classic CAS · Exact area
Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.
Type the integral command with the function, the variable, and both limits: area under x² from 0 to 3. Press enter.
integral(x^2▶,x,0,3)enter
You should seeintegral(x^2,x,0,3) 9
Tips
- If the answer is negative, part of the curve sits below the x-axis. Split the interval at each zero to get the true area.