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Math Help - Iterated Integral

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    Iterated Integral

    Use an Iterated Integral to find the area of the region bounded by the graphs of the equation.

    x^2+y^2=4 , x=0 , y=0
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    Setup:
    \int_0^4 \left(\int_0^{\sqrt{4-y^2}} dx \right) dy
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    Quote Originally Posted by asdf122345 View Post
    Use an Iterated Integral to find the area of the region bounded by the graphs of the equation.

    x^2+y^2=4 , x=0 , y=0
    If x^2 + y^2 = 4

    then y = \pm \sqrt{4 - x^2}.


    Also note, that since you are bounded by x = 0 and y = 0, you are stuck in the first quadrant, so we only take the positive square root. Also note that in this region, we have 0 \leq x \leq 4 and 0 \leq y \leq 4.


    Therefore we are trying to find

    \int_0^2{\sqrt{4 - x^2}\,dx}.
    Last edited by Prove It; March 25th 2010 at 10:29 PM.
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    Shouldn't it go from 2 to 0?
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    Quote Originally Posted by asdf122345 View Post
    Shouldn't it go from 2 to 0?
    Yes, yes it should. For a much easier time, convert it to polar coordinates
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