Area of a region between x^4 - 4x^2 and x^2 - 4

[lmerry]

\(\displaystyle f(x)=x^4-4x^2\)
\(\displaystyle g(x)=x^2-4\)

resulting in a graph like:

so i can't figure out how to set up the integral so i get the right area. Thanks in advance for helping.

 

[arthur ohlsten]

eq1) y=x^2[x^2-4]
eq2) y=x^2-4

where do the curves cross?
x^2[x^2-4]=[x^2-4]
[x^2-4][x^2-1]=0
[x-2][x+2][x-1][x+1]=0
x=2,-2,1,-1

the curves are symmetric about the y axis.
We will only determine the area to the right of the y axis and double the result

1/2 area =S [0,1] [eq1-eq2]dx + S [1,2] [eq2-eq1]dx + S [2,oo] int[eq1-eq2]dx


eq1-eq2=x^4-4x^2-x^2+4
eq1-eq2=x^4-5x^2+4
eq2-eq1=-[x^4-5x^2+4]

The rest is left to the student.
I hated those words when a student
Arthur