Integration (AQA A-Level Mathematics): Flashcards

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Definite Integration
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Result of definite integration

Specific numerical value

Fundamental Theorem of Calculus

∫abf(x)dx=F(b)−F(a)\int_a^b f(x) dx = F(b) - F(a)

Net area meaning in definite integrals

Areas below x-axis subtract from total

Finding total area regardless of sign

Integrate absolute value of function

∫abf(x)dx\int_a^b f(x) dx with reversed limits

−∫baf(x)dx-\int_b^a f(x) dx

Value of ∫aaf(x)dx\int_a^a f(x) dx

00

Additivity property formula

∫abf(x)dx+∫bcf(x)dx=∫acf(x)dx\int_a^b f(x) dx + \int_b^c f(x) dx = \int_a^c f(x) dx

Constant cc in definite integration

Always cancels

aa and bb in ∫abf(x)dx\int_a^b f(x) dx

Limits of integration

Definite integral physics applications

Displacement, work, energy

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