Integration

Integration as reverse differentiation, including basic anti-derivatives, definite integrals, area under and between curves, substitution, and applications to displacement and distance.

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Definite Integrals, Areas, and Basic Anti-Derivatives

Integration

Evaluating definite integrals ∫abf(x)dx=F(b)−F(a), using anti-derivatives ∫f(x)dx=F(x)+C and the power rule ∫xndx=n+1xn+1+C for n=−1, with linearity, splitting or combining intervals, boundary conditions, and finding areas under a curve, between a curve and the x-axis, or between two curves using ∣f(x)∣ and ∣f(x)−g(x)∣.

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Anti-Derivative Rules

Integration

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Techniques of Integration

Integration

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Kinematics

Integration

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Integration

Integration as reverse differentiation, including basic anti-derivatives, definite integrals, area under and between curves, substitution, and applications to displacement and distance.

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Choose a concept to study or jump straight into the problem bank.

Concepts

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Definite Integrals, Areas, and Basic Anti-Derivatives

Integration

Evaluating definite integrals ∫abf(x)dx=F(b)−F(a), using anti-derivatives ∫f(x)dx=F(x)+C and the power rule ∫xndx=n+1xn+1+C for n=−1, with linearity, splitting or combining intervals, boundary conditions, and finding areas under a curve, between a curve and the x-axis, or between two curves using ∣f(x)∣ and ∣f(x)−g(x)∣.