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13 cards from this deck
Definite integration
∫abf(x) dx\int_a^b f(x) \, dx∫abf(x)dx
Net area between curve and xxx-axis
When f(x)≥0f(x) \geq 0f(x)≥0 for all xxx in [a,b][a,b][a,b]
Negative of area (integral negative)
Positive area minus negative area
Set up integral with f(x)f(x)f(x) and [a,b][a,b][a,b]
Find antiderivative F(x)F(x)F(x) of f(x)f(x)f(x)
F(b)−F(a)F(b) - F(a)F(b)−F(a)
Take absolute value: ∣∫abf(x)dx∣|\int_a^b f(x) dx|∣∫abf(x)dx∣
∫ab[f(x)−g(x)]dx\int_a^b [f(x)-g(x)]dx∫ab[f(x)−g(x)]dx where f(x)≥g(x)f(x) \geq g(x)f(x)≥g(x)
Integrate each part separately, use absolute values
Distance from 0 (magnitude/length)
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