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anonymous

  • 5 years ago

Find the area between the graphs of x=2y^2 and x=12-y^2

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  1. anonymous
    • 5 years ago
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    To find the area between the graphs you'll have to first re-write the given equations in terms of y :) 1) Sketch both functions in a graph 2) Find the intersection points when y1 = y2 --> this will yeild you the intervals ^_^ 3) Then subtract the curve that's on the top from the curve that's on the bottom; you can find out which is on the top and which is on the bottom from the graph. General equationf of finding the area between the graphs is : \[A = \int\limits_{a}^{b} g(x) - f(x) dx\] where g(x) is the curve that's in the top, and f(x) is the curve that's in the bottom ^_^ I hope this helps because it'll take me ages to solve the problem :) give it a one more try

  2. anonymous
    • 5 years ago
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    You don't have to re-write it in terms of y. Keep them as they are.. find the intersection points, that's: \[2y^2=12-y^2 \implies y=2, y=-2\] If you draw them, you will see that 12-y^2 is "on the right" of 2y^2 in the given interval, so your area will be: \[A=\int\limits\limits_{-2}^{2}(12 - y^2 -2y^)dy =\int\limits\limits_{-2}^{2}(12-3y^2) dy=12y-y^3=32\]

  3. anonymous
    • 5 years ago
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    Does that make sense to you, Ebrake?

  4. anonymous
    • 5 years ago
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    yea when i did it out I got 32 but i just wanted to make sure.

  5. anonymous
    • 5 years ago
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    Hey sstarica, Where have you been? long time no see.

  6. anonymous
    • 5 years ago
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    lol, here and there, everywhere? :)

  7. anonymous
    • 5 years ago
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    You're the one whose been out of sight lol

  8. anonymous
    • 5 years ago
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    LOL.. I guess you're right :)

  9. anonymous
    • 5 years ago
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    I'm good, how abt you ^_^?

  10. anonymous
    • 5 years ago
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    I am fine.. Thanks for asking ^^

  11. anonymous
    • 5 years ago
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    I got around 42.6 unless I read the integral wrong: A=∫−22(12−y2−2y)dy = ∫−22(12y−(1/3y^3)−y^2)dy = [12y−(1/3y^3)−y^2] from -2 to 2 then you just subsitute in 2 for y and substitute in -2 for y and then subtract one from the other and you get around 42.6

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