v = 2π x [(9 − x^2 ) − (9 − 3x)]
Graphing Calculator (TI-83 and TI-84)
Press the Y= button, and enter the following values to the list:
Y 1 = 9 − x^2
Y 2 = 9 − 3x
Press 2nd and MODE to view the home screen.
Press MATH and select 9: fnInt from the list, then enter the following:
fnInt(2π X(Y 1 − Y 2 ), X, 0, 2)
• Press VARS and go to Y-VARS to select the variables Y 1 and Y 2.
The result is 25.13274123. Divide that by π to get 8, (C).
Step 2: We are being asked to rotate this region around the y-axis, and both of the functions are
in terms of x, so we should use the method of shells. We use this method whenever we take a
vertical slice of a region and rotate it around an axis parallel to the slice (review the unit if you
are not sure what it means). This will give us a region that looks like the following: