University⏱ 4 min

Area Between Curves

Integral between two functions

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x^22xA=1.333
A=∫ab(g−f) dx=∫02(2x−x2) dx=1.333A = \int_a^b (g-f)\,dx = \int_{0}^{2} (2x-x^2)\,dx = 1.333

Area between curves = integral of (top - bottom). The blue shaded region is the result of integrating between intersection points.