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To find the area of the region, first you must find where the two graphs intersect.
This happens at x = 0 and 1.
Therefore the area is the integral of the top function - the bottom function from 0 to 1. So we have:
Integral(sqrt x - x^2)dx.
If you have this ability on the graphing calculator, you can do it that way, or by hand we have:
2/3x^(3/2) - 1/3x^3 after integrating, then plugging in f(b) - f(a) for the interval (0,1) we have:
[2/3(1)^(3/2)] - 1/3(1)^3] - [2/3(0)^(3/2)] - 1/3(0)^3] = 2/3 - 1/3
= 1/3 square units
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