Difference between revisions of "009B Sample Final 2, Problem 3"

Revision as of 20:10, 17 February 2017

Find the volume of the solid obtained by rotating the region bounded by the curves $y=x$ and $y=x^{2}$ about the line $y=2.$

Solution:

(a)

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

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-<span class="exam">Consider the region bounded by the following two functions:
+<span class="exam">Find the volume of the solid obtained by rotating the region bounded by the curves <math>y=x</math> and <math>y=x^2</math> about the line <math>y=2.</math>
-::::::::<span class="exam"> <math style="vertical-align: -5px">y=2(-x^2+9)</math> and <math style="vertical-align: -4px">y=0</math>.
-<span class="exam">a) Using the lower sum with three rectangles having equal width, approximate the area.
-<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.
-<span class="exam">c) Find the actual area of the region.
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