Difference between revisions of "Prototype Calculus Question"

From Math Wiki
Jump to navigation Jump to search
Line 26: Line 26:
 
!Step 2:  
 
!Step 2:  
 
|-
 
|-
|Since our rectangles will be trapped between the two functions, and will be rotated around the ''x''-axis (where <math> y=0 </math>,) we find
+
|Since our rectangles will be trapped between the two functions, and will be rotated around the ''x''-axis (where <math> y=0 </math>), we find
 
|-
 
|-
 
|the inner radius is <math style="vertical-align:0%;"> r = 5-x </math>, represented by the blue line, while
 
|the inner radius is <math style="vertical-align:0%;"> r = 5-x </math>, represented by the blue line, while

Revision as of 11:37, 8 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...