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

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::<span class="exam">a) Find the area of the surface obtained by rotating the arc of the curve  
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<span class="exam">(a) Find the area of the surface obtained by rotating the arc of the curve  
  
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::::<math>y^3=x</math>
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::<math>y^3=x</math>
  
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::<span class="exam">between <math>(0,0)</math> and <math>(1,1)</math> about the <math>y</math>-axis.
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<span class="exam">between <math>(0,0)</math> and <math>(1,1)</math> about the <math>y</math>-axis.
  
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::<span class="exam">b) Find the length of the arc  
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<span class="exam">(b) Find the length of the arc  
  
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::::<math>y=1+9x^{\frac{3}{2}}</math>
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::<math>y=1+9x^{\frac{3}{2}}</math>
  
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::<span class="exam">between the points <math>(1,10)</math> and <math>(4,73).</math>
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<span class="exam">between the points <math>(1,10)</math> and <math>(4,73).</math>
  
 
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'''Solution:'''
 
'''Solution:'''
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Revision as of 18:21, 18 February 2017

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

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 y^3=x}

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

(b) Find the length of the arc

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

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

Foundations:  


Solution:

(a)

Step 1:  
Step 2:  

(b)

Step 1:  
Step 2:  

(c)

Step 1:  
Step 2:  


Final Answer:  
(a)
(b)
(c)

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