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10 cards from this deck
Net signed area under curve
A=∫abf(x) dxA = \int_a^b f(x) \, dxA=∫abf(x)dx
A=−∫abf(x) dxA = -\int_a^b f(x) \, dxA=−∫abf(x)dx
Integral gives negative value but area must be positive
Reverse limits: A=∫baf(x) dxA = \int_b^a f(x) \, dxA=∫baf(x)dx
Split integral at crossing point, add absolute values
Sign of f(x)f(x)f(x) in the given interval
Yes, area must always be positive
Whether curve is above or below x-axis
A=∫cbf(x)dx+(−∫acf(x)dx)A = \int_c^b f(x)dx + (-\int_a^c f(x)dx)A=∫cbf(x)dx+(−∫acf(x)dx)
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