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

@@ Line 3: / Line 3: @@
 ::<math>y^3=x</math>
-<span class="exam">between <math style="vertical-align: -5px">(0,0)</math> and <math style="vertical-align: -5px">(1,1)</math> about the <math style="vertical-align: -4px">y</math>-axis.
+<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">(b) Find the length of the arc
@@ Line 9: / Line 9: @@
 ::<math>y=1+9x^{\frac{3}{2}}</math>
-<span class="exam">between the points <math style="vertical-align: -5px">(1,10)</math> and <math style="vertical-align: -5px">(4,73).</math>
+<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>
-{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
+<hr>
-!Foundations: &nbsp;
+[[009B Sample Final 2, Problem 5 Solution|'''<u>Solution</u>''']]
-|-
-|'''1.''' The formula for the length &nbsp;<math style="vertical-align: 0px">L</math>&nbsp; of a curve &nbsp;<math style="vertical-align: -5px">y=f(x)</math>&nbsp; where &nbsp;<math style="vertical-align: -3px">a\leq x \leq b</math>&nbsp; is
-|-
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-&nbsp; &nbsp; &nbsp; &nbsp;<math>L=\int_a^b \sqrt{1+\bigg(\frac{dy}{dx}\bigg)^2}~dx.</math>
-|-
-|'''2.''' The surface area &nbsp;<math style="vertical-align: 0px">S</math>&nbsp; of a function &nbsp;<math style="vertical-align: -5px">y=f(x)</math>&nbsp; rotated about the &nbsp;<math style="vertical-align: -4px">y</math>-axis is given by
-|-
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-&nbsp; &nbsp; &nbsp; &nbsp;<math style="vertical-align: -13px">S=\int 2\pi x\,ds,</math>&nbsp; where <math style="vertical-align: -18px">ds=\sqrt{1+\bigg(\frac{dy}{dx}\bigg)^2}.</math>
-|}
-'''Solution:'''
+[[009B Sample Final 2, Problem 5 Detailed Solution|'''<u>Detailed Solution</u>''']]
-'''(a)'''
-{| 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;"
-!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;"
-!Step 2: &nbsp;
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-!Final Answer: &nbsp;
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 [[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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