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

1. ## 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

2. ## 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?

3. ## Re: use double integration to find the area of the plane region enclosed by given cur

Originally Posted by math951
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.