Difference between revisions of "Prototype Calculus Question"

From Math Wiki
Jump to navigation Jump to search
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 18:03, 1 March 2015

9BSF1 3a.png

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...