Find area by graphing/integrating
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Find area by graphing/integrating

[From: ] [author: ] [Date: 11-07-05] [Hit: ]
533333..........
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?

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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
1
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