Juggler123
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I need to find the area between the parabolas x=y^2 and x=2y-y^2, I know I need to use a double integral but am having difficulty finding the limits. Can anyone help please?
Finding the Area Between Parabolas: Double Integral Help Needed
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Hi Juggler123! 
(try using the X2 tag just above the Reply box
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No, for an area you'll only need a single integral …
divide the area into strips of width dy, find the area of each strip, and integrate over y.
(try using the X2 tag just above the Reply box
)Juggler123 said:
No, for an area you'll only need a single integral …
divide the area into strips of width dy, find the area of each strip, and integrate over y.
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Well, you certainly could use a double integral to find area!
The double integral
[itex]\int_{x=a}^b \int_{y= f(x)}^{g(x)} 1 dy dx[/itex]
has a very simple first integral of f(x)- g(x) so that the second integral is
[itex]\int_{x=a}^b f(x)- g(x) dx[/itex]
and that is the integral for area between the curves that tiny-tim is referring to.
So, for your problem, first, determine for what values of x the graphs intersect. That will be your limits of integration a and b for the "outer" integral (a being the smaller, b the larger, of course). The decide which of the graphs is higher inside that interval. That will be f(x) and g(x), the limits of integration for the "inner" integral.
The double integral
[itex]\int_{x=a}^b \int_{y= f(x)}^{g(x)} 1 dy dx[/itex]
has a very simple first integral of f(x)- g(x) so that the second integral is
[itex]\int_{x=a}^b f(x)- g(x) dx[/itex]
and that is the integral for area between the curves that tiny-tim is referring to.
So, for your problem, first, determine for what values of x the graphs intersect. That will be your limits of integration a and b for the "outer" integral (a being the smaller, b the larger, of course). The decide which of the graphs is higher inside that interval. That will be f(x) and g(x), the limits of integration for the "inner" integral.