|
|
| Line 1: |
Line 1: |
| − | [[File:9BSF1 3a.png|250px|right]] | + | [[File:9BSF1 3a.png|270px|right]] |
| | | | |
| | Find the volume of the solid obtained by rotating the area enclosed by <math> y=5-x </math> and <math style="vertical-align:-17%;"> y=25-x^2 </math> <br> around the ''x''-axis. | | Find the volume of the solid obtained by rotating the area enclosed by <math> y=5-x </math> and <math style="vertical-align:-17%;"> y=25-x^2 </math> <br> around the ''x''-axis. |
Revision as of 19:03, 1 March 2015
Find the volume of the solid obtained by rotating the area enclosed by 
and 
around the x-axis.
| Foundations
|
| • 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.
|
Solution:
| 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...
|
