use a graphing utility to graph the region bounded by the graphs of the functions, and use the integration capabilities of the graphing utility to find the area of the region
y=x^4-2x^2
y=2x^2
how do i go about doing this?
y=x^4-2x^2
y=2x^2
how do i go about doing this?
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Graph the two functions, and find the points of intersection. The curves intersect at (-2, 8), (0, 0) and (2, 8). Using symmetry, we can find the area from x = 0 to x = 2, and double the result.
dA = (y 2 - y1) dx = [(2x^2 - (x^4 - 2x^2)] dx = (4x^2 - x^4) dx
1/2 A = ∫ {0, 2} (4x^2 - x^4) dx = 4.2666666....
A = 8.533333.... = 128/15
dA = (y 2 - y1) dx = [(2x^2 - (x^4 - 2x^2)] dx = (4x^2 - x^4) dx
1/2 A = ∫ {0, 2} (4x^2 - x^4) dx = 4.2666666....
A = 8.533333.... = 128/15