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Areas Under a Curve

  1. Apr 4, 2015 #1
    Find the area of the regions shown in the figures.

    These are the graphs used :

    y = x^2
    x = 2 Sin ^2 (y)

    I know that I need to set the two equations equal to each other in order to find the points of intersection, but I run into some trouble when trying to simplify it for y.

    This is what I tried

    Since y=x^2
    Sqrt.(y)= x

    So now I have
    x= Sqrt.(y)
    x= 2 Sin ^2 (y)

    Sqrt.(y) - 2 Sin ^2 (y) = 0

    So based on the graph that I am given in the book I can't really tell which is the top or right curve to subtract the bottom or left curve.

    After this step I would square both sides and be left with (Sqrt.(y) -2 Sin(^2y)^2) = 0, but I am not sure if that is allowed. Not sure on how to proceed from here. I would appreciate some help. Thanks!
  2. jcsd
  3. Apr 5, 2015 #2


    User Avatar
    Science Advisor

    Hint: [itex] cos(2y)=1-2sin^{2}(y)[/itex]. Rearrange and find y as a function of x.
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