Difference between revisions of "Prototype Calculus Question"
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(Created page with "250px|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...") |
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|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. | ||
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− | | | + | |Using the determined values, set up and solve the integral. |
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− | |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. | + | |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. |
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Revision as of 17:54, 1 March 2015
Find the volume of the solid obtained by rotating the area enclosed by and
around the x-axis.
Foundations |
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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: |
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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: |
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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: |
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We must set the two functions equal, and solve. More to follow... |