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Area of an enclosed region

  1. May 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region enclosed by y = [tex]\sqrt[3]{x}[/tex], the tangent line to this curve at x = 8, and the y-axis.


    2. Relevant equations
    Definate integral properties, fundamental theorem of calculus



    3. The attempt at a solution
    I know and understand what the question is asking for--find the area of the region--i'm just having problems actually finding the region I need to calculate. I can't seem to figure out what they want through the tangent line; do I need to simply take the derivative of [tex]\sqrt[3]{x}[/tex] and use it, plug in x=8 into the derivative and then use it, or do something completely different? Any help you can guys can give to point me in the right direction here would be greatly appreciated, thanks in advance.
     
  2. jcsd
  3. May 16, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    It might be easier if you think of the function as x= y3. Then dx/dy= 3y2 so dy/dx= 1/(3y). Now what is y when x= 8?
     
  4. May 16, 2009 #3

    Cyosis

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    Homework Helper

    Find the equation for the tangent line, then draw both the tangent line and y on the same axes. It will be obvious from there which region you want to calculate.

    It will look like this:

    http://img29.imageshack.us/img29/32/region.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
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