Difference between revisions of "Prototype Calculus Question"

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

Revision as of 18:59, 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...