Calc 2 help

[Stuff_]

I'm a bit stumped with my calculus 2 homework.

 

My professor is Russian, with a thick accent. So every few words I have no idea what she is actually saying.

 

Anyway, I have this problem:

 

(1 point) Find the area of the plane region enclosed by the graphs of the functions:

2x = y^2, x + y = 4, x + y = 12

 

I have drawn out the functions and found the region, but I'm not sure where to go from here.

 

The book provides examples using 2 functions, but I can't find any examples using 3 functions.

 

Any help would be appreciated. 

[Jaybird]

Ya profs always give you questions with more variables and junk than the book examples use. Can't say I coverted this material in my cal 2 class.

[ilikemacandpc]

Split it into multiple areas that are bounded by only two functions. Make them all as functions of y and integrate with respect to y . 

 

http://tutorial.math.lamar.edu/Classes/CalcI/AreaBetweenCurves.aspx

 

Look at example 6. 

[Stuff_]

This is what the graph looks like:

http://imgur.com/yXJyThD

 

And the region is in purple.

Where would I split the region at? Which point, that is. 

[TideRower]

Calculate the intersection points.

Integrate sqrt(2x) - the positive red graph- between the two intersection points with positve y-values. Then you subtract the region of a triangle on the left and at one on the right side.

Then you have the region above the x-axis. Calculating the region below goes analog e.g. mirroring the graph.