Prototype Calculus Question

From Math Wiki
Revision as of 19:03, 1 March 2015 by MathAdmin (talk | contribs)
Jump to navigation Jump to search
9BSF1 3a.png

Find the volume of the solid obtained by rotating the area enclosed by and
around the x-axis.

• Choose either shell or washer method.
• Find the appropriate radii.
• Determine the bounds of integration by finding when both functions have the same y value.
• Using the determined values, set up and solve the integral.


Step 1:
Since we are rotating around the x-axis, the washer method would utilize tall rectangles with dx as their width. This seems like a reasonable choice, as these rectangles would be trapped between our two functions, allowing us to solve a single integral.
Step 2:
Since our rectangles will be trapped between the two functions, and will be rotated around the x-axis (where ,) we find
the inner radius is , represented by the blue line, while
the outer radius is , represented by the red line.
Step 3:
We must set the two functions equal, and solve. More to follow...