Integration as the reverse of differentiation, integrating x^n, finding constants of integration.
First principles, differentiating x^n, gradient functions, rates of change.
Evaluating definite integrals, area under a curve, area between curves.
Using substitution to integrate composite functions, reversing the chain rule.
Integration by parts formula, choosing u and dv, repeated application.
Integrating sin, cos, tan, sec² and their compositions. Using trig identities to integrate.
Using partial fraction decomposition to integrate rational functions.
Using differentiation and integration for variable acceleration, displacement-velocity-acceleration relationships.