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Weird integral question

  1. May 18, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the integral of sqrt(9-x^2) over [0,3]. You will not be able to find an antiderivative, so instead interpret the definite integral as the area of a region and compute the area geometrically (I haven't reached integration by substitution and integration by parts in class yet).



    2. Relevant equations
    The part i'm lost on



    3. The attempt at a solution
    This question has me stumped. I tried using both riemann sums and the trapezoid method but this didn't get me anywhere, as the answer is supposed to be 9pi/4. It is only out of 1 mark, so I know it can't be that difficult, but i'm still lost over it. Any pointers in the right direction here would be greatly appreciated. Thanks in advance.
     
  2. jcsd
  3. May 18, 2009 #2

    Pyrrhus

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    Are you familiar with this geometry figure [itex] y^2 + x^2 = 3^2 [/itex] ? Now consider what the square root does to this relation? (this is not a function), but when [itex] y = \sqrt{3^2 - x^2} [/itex] what happens? (think in terms of Real value [itex] \sqrt{x} [/itex] function)
     
    Last edited: May 18, 2009
  4. May 18, 2009 #3
    Try downloading the program Geogebra (Web Start) - it's free math software, then let it draw the graph of this "weird" thing. You'll probably see what the answer is..
     
  5. May 18, 2009 #4
    No I have not heard of that geometric figure before, but I do know that the square root prevents the function from crossing zero and becoming a negative number, and in a sense resembles half of a horizontal parabola. Now for the obvious question, how does that help me? :tongue:
     
  6. May 18, 2009 #5

    Redbelly98

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    Okay, how about

    x2 + y2 = r2

    Is that figure more familiar to you?
     
  7. May 18, 2009 #6
    Ohh it's a circle, I see it now, the radius is 3 so I just need to use the area formula and divide the answer by 4. Thanks for all the help guys :smile:
     
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