Difference between revisions of "Prototype Calculus Question"

From Math Wiki
Jump to navigation Jump to search
Line 4: Line 4:
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Foundations
+
! Foundations  
 
|-
 
|-
 
|• Choose either shell or washer method.
 
|• Choose either shell or washer method.
Line 18: Line 18:
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 1:
+
!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.
 
|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.
Line 24: Line 24:
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!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
Line 34: Line 34:
  
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Step 3:
+
!Step 3: &nbsp;
 
|-
 
|-
 
|We must set the two functions equal, and solve.  More to follow...
 
|We must set the two functions equal, and solve.  More to follow...
 
|}
 
|}

Revision as of 20:05, 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...