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Thread: use double integration to find the area of the plane region enclosed by given curve

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    use double integration to find the area of the plane region enclosed by given curve

    y^2=-x and 3y-x=4

    I am setting up the double integral as dxdy,


    for the dx limit I have 3y-4 on bottom and -y^2 and top, and I understand that. However, I see the solution guide for dy limit has -4 to 1, and I am not understanding how they get that?

    solution: Calculus (9780470647721), Pg. 1016, Ex. 30 :: Homework Help and Answers :: Slader
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    Re: use double integration to find the area of the plane region enclosed by given cur

    I see why it has the limits from -4 to 1 on dy... for instance, x=3y-4..... for x=3(5)-4.... we get x=11.. and that is not in the region. But how the hell was I suppose to know that lmao?
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    Re: use double integration to find the area of the plane region enclosed by given cur

    Quote Originally Posted by math951 View Post
    y^2=-x and 3y-x=4

    I am setting up the double integral as dxdy,


    for the dx limit I have 3y-4 on bottom and -y^2 and top, and I understand that. However, I see the solution guide for dy limit has -4 to 1, and I am not understanding how they get that?

    solution: Calculus (9780470647721), Pg. 1016, Ex. 30 :: Homework Help and Answers :: Slader
    Solve the second equation for x and put it in the first equation. Solve the resulting quadratic for y. You should get -4 and 1.
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