Integration

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

Sign up to view your learning progress

Sign up

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

Concepts

Start Here

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)∣.

Thumbnail for Definite Integrals, Areas, and Basic Anti-Derivatives

0/4 key exercises

Anti-Derivative Rules

Integration

0/1 key exercises

Techniques of Integration

Integration

0/3 key exercises

Kinematics

Integration

0/3 key exercises

Integration

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

Sign up to view your learning progress

Sign up

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

Concepts

Start Here

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)∣.