Calculating the area between two curves

[physstudent1]

Homework Statement

Compute the area between the two functions as an integral along the x-axis or the y-axis:

x=abs(y)
x=6-y^2

Homework Equations

The Attempt at a Solution

I sketched the graph to determine which was to the right and which was left finding out that 6-y^2 is to the right then I found out where the limits of integration would be and go the to be +sqrt6 , -sqrt6 however I'm not getting the correct answer and I'm unsure of how to integrate the absolute value function, I tried to split it up into two separate integrals but it didn't work

 

[malty]

The integral of an absolute value is the signum function, are you familar with it?
(Just in case)
http://en.wikipedia.org/wiki/Sign_function

How did you get the limits of integration??

 

[physstudent1]

Ah, I see no I was not familiar with that function, I got my limits because those are the points where the parabola meets the y axis,

 

[malty]

Ah, I see no I was not familiar with that function, I got my limits because those are the points where the parabola meets the y axis,

But where does the curve intersect the line?

 

[HallsofIvy]

Homework Statement

Compute the area between the two functions as an integral along the x-axis or the y-axis:

x=abs(y)
x=6-y^2

Homework Equations

The Attempt at a Solution

I sketched the graph to determine which was to the right and which was left finding out that 6-y^2 is to the right then I found out where the limits of integration would be and go the to be +sqrt6 , -sqrt6 however I'm not getting the correct answer and I'm unsure of how to integrate the absolute value function, I tried to split it up into two separate integrals but it didn't work

There isn't "one function to the right and the other to the left". There is one function above the other!