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Suppose the problem is: Find the area enclosed by curves (y = x^2) and (y = 2x - x^2).
Set (x^2 = 2x - x^2):
[2x^2 - 2x = 0 \implies 2x(x-1) = 0 \implies x=0 \text{ or } x=1]
For (0 < x < 1), take (x=0.5):
Area (A = \int{0}^{1} [\text{upper function} - \text{lower function}] dx):
[A = \int{0}^{1} (2x - x^2 - x^2) dx = \int_{0}^{1} (2x - 2x^2) dx]
Antiderivative of (2x) is (x^2), antiderivative of (2x^2) is (\frac{2}{3}x^3):
[A = \left[ x^2 - \frac{2}{3}x^3 \right]_0^1 = (1 - \frac{2}{3}) - (0 -0) = \frac{1}{3}]
Answer: (\boxed{\frac{1}{3}})
Please share your specific problem, and I will help you solve it!
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