Difference between revisions of "009B Sample Final 2, Problem 5"

Latest revision as of 17:28, 2 December 2017

(a) Find the area of the surface obtained by rotating the arc of the curve

y^{3}=x

between $(0,0)$ and $(1,1)$ about the $y$ -axis.

(b) Find the length of the arc

y=1+9x^{\frac {3}{2}}

between the points $(1,10)$ and $(4,73).$

Solution

Detailed Solution

Return to Sample Exam

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-<span class="exam">Consider the region bounded by the following two functions:
+<span class="exam">(a) Find the area of the surface obtained by rotating the arc of the curve
-::::::::<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.
+::<math>y^3=x</math>
-<span class="exam">b) Using the upper sum with three rectangles having equal width, approximate the area.
+<span class="exam">between &nbsp;<math style="vertical-align: -5px">(0,0)</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">(1,1)</math>&nbsp; about the &nbsp;<math style="vertical-align: -4px">y</math>-axis.
-<span class="exam">c) Find the actual area of the region.
+<span class="exam">(b) Find the length of the arc
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+::<math>y=1+9x^{\frac{3}{2}}</math>
-!Foundations: &nbsp;
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-'''Solution:'''
+<span class="exam">between the points &nbsp;<math style="vertical-align: -5px">(1,10)</math>&nbsp; and &nbsp;<math style="vertical-align: -5px">(4,73).</math>
-'''(a)'''
+<hr>
+[[009B Sample Final 2, Problem 5 Solution|'''<u>Solution</u>''']]
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+[[009B Sample Final 2, Problem 5 Detailed Solution|'''<u>Detailed Solution</u>''']]
-!Step 2: &nbsp;
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-'''(b)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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-'''(c)'''
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Step 1: &nbsp;
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
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-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
-!Final Answer: &nbsp;
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-|'''(a)'''
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-|'''(c)'''
-|}
 [[009B_Sample_Final_2|'''<u>Return to Sample Exam</u>''']]

Difference between revisions of "009B Sample Final 2, Problem 5"

Latest revision as of 17:28, 2 December 2017

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