- #1

mathelord

## Main Question or Discussion Point

when three curves intersect,i mean like the intersection of three straight lines to give a triangle,how can one find the area between the curves

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- #1

mathelord

when three curves intersect,i mean like the intersection of three straight lines to give a triangle,how can one find the area between the curves

- #2

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area of a triangle is given by 1/2 * b * h

- #3

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I think mathelord means any three curves. You can use a double integral. Do you know calculus?

- #4

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If you don't know calculus you calculate the height. The factor of two perpendicular slopes is -1.

- #5

HallsofIvy

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Exactly how that is done depends on the curves themselves. In the very common situation, a sort of "curvy" triangle, where you have one curve under the other two (between the points where the other two intersect it), then you don't need a double integral. You will need to break the integral into two parts. I'm going to call the curve on the bottom C1, the graph of y= f1(x), and the other two C1 and C2, graphs of y=f2(x), y= f3(x) respectively. Let's say that C2 intersect C1 at x=a, C3 intersects C1 at x= c, and that C2 is below C3 until they intersect at x= b after which C3 is below C2.

Then the area is given by two separate integrals:

[tex]\int_a^b(f2(x)-f1(x))dx+ \int_b^c(f3(x)-f1(x)dx[/tex]

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