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

Revision as of 10:18, 3 March 2017

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

Foundations:
1. You can find the intersection points of two functions, say $f(x),g(x),$
by setting $f(x)=g(x)$ and solving for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x.}
2. The volume of a solid obtained by rotating a region around the $x$ -axis using disk method is given by
$\int \pi r^{2}~dx,$ where $r$ is the radius of the disk.

Solution:

Final Answer:

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;
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+|'''1.''' You can find the intersection points of two functions, say &nbsp; <math style="vertical-align: -5px">f(x),g(x),</math>
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+&nbsp; &nbsp; &nbsp; &nbsp; by setting &nbsp;<math style="vertical-align: -5px">f(x)=g(x)</math>&nbsp; and solving for &nbsp;<math style="vertical-align: 0px">x.</math>
+|-
+|'''2.''' The volume of a solid obtained by rotating a region around the &nbsp;<math style="vertical-align: 0px">x</math>-axis using disk method is given by
+|-
+|
+&nbsp; &nbsp; &nbsp; &nbsp; <math style="vertical-align: -13px">\int \pi r^2~dx,</math>&nbsp; where &nbsp;<math style="vertical-align: 0px">r</math>&nbsp; is the radius of the disk.
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