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Home > CALC > Chapter 8 > Lesson 8.3.1 > Problem 8-101
The graph at right is
The
-axis. Vertical rectangles.
The
-axis. Horizontal rectangles would be very difficult (because the inverse of
is NOT a function). So use the Shell Method. The line
. By shells:
Where did the
come from?
Recall that each cylindrical shell is a prism with dimensions: (base)(height)(width).
Well,represents the (radius) in the circumference part of the formula: .
If we were rotating about the-axis (as in part (b)), then the radius would be the same as the bounds, .
But since we are rotating about a line that is parallel to the-axis, we do not want the radius to be the same as the bounds.
When we plug in the lower bound, we actually want a radius that is .
And when we plug in the upper bound, we actually want a radius that is .
will make this work! The line
. Vertical rectangles with a hole in the center.