Difference between revisions of "009B Sample Final 3, Problem 4"

Revision as of 10:57, 18 February 2017

Find the volume of the solid obtained by rotating about the $x$ -axis the region bounded by $y={\sqrt {1-x^{2}}}$ and $y=0.$

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 about the <math>x</math>-axis the region bounded by <math>y=\sqrt{1-x^2}</math> and <math>y=0.</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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