Find the area of the region bounded by

Question

anonymous · Answer

$$y = x ^{4} - 4x ^{2}  and  y = x ^{3} -4x$$

anonymous · Answer

draw them out first
find the intersections, 
consider which graph is on top/ bottom on each interval
take integral for each of them
add them together.

anonymous · Answer

This is the graph, so that 
in [-2,0] $x^3-4x$ on top and $x^4 -4x^2$ is in bottom
The area of this interval is 
$$\int_{-2}^0 (x^3-4)-(x^4-4x^2) dx$$ solve for it, you have the results of this interval, let say r1
Do the same with the second interval [0,1]. Pay attention, at this interval, x^4-4x^2 is on top. 
Do the same with 3rd one and 4th one,
Add them together

anonymous · Answer

https://www.desmos.com/calculator/0m1gzh0k7g