Question

Find the area of the region bounded by

Answer 1

\[y = x ^{4} - 4x ^{2} and y = x ^{3} -4x\]

Answer 2

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.

Answer 3

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

Answer 4

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