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Math Help - area between curves

  1. #1
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    area between curves

    x=y^2 + 2

    y=0
    y=3
    x=0

    find the area..

    can anybody help me start this problem?
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  2. #2
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    Quote Originally Posted by FinalFantasy9291 View Post
    x=y^2 + 2

    y=0
    y=3
    x=0

    find the area..

    can anybody help me start this problem?
    This is the area of the curve against the y-axis from y=0 to y=3
    x=0 is the y-axis.

    \int_{y=0}^3f(y)dy=\int_{y=0}^3\left(y^2+2\right)d  y
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  3. #3
    Senior Member AllanCuz's Avatar
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    Quote Originally Posted by FinalFantasy9291 View Post
    x=y^2 + 2

    y=0
    y=3
    x=0

    find the area..

    can anybody help me start this problem?
    This is a parabola in the XY plane and your bounds are given. So lets set this up

    \int_0^3 dy \int_0^{y^2 + 2} dx

    Where does this come from? Well we are bounded by the x function and the co-ordinate planes. So clearly, our dx integral is from 0-->function. Likewise, y is bounded by the co-ordinate axis and a function, but in this case that function is 3. Thus our bounds are from 0-->3

    You can also switch the limits of integration here and compute dy first before dx.
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