Integration
Anti-differentiation, definite integrals, area and core integration techniques.
Integration toolkit
Integration reverses differentiation and is also used to calculate signed area under a curve.
Power rule\[\int x^n\,dx=\frac{x^{n+1}}{n+1}+C,\quad n\ne -1\]
Linearity\[\int(af(x)+bg(x))\,dx=a\int f(x)\,dx+b\int g(x)\,dx\]
Choose a method
Exam-ready integration pages.
Calculus
Integration by Substitution
Reverse chain rule and change of variables.
CalculusIntegration by Parts
Reverse product rule technique.
CalculusDefinite Integrals
Signed area and integral properties.
CalculusArea Under a Curve
Total area and signed area.
CalculusArea Between Two Curves
Upper curve minus lower curve.
Calculus / AITrapezoidal Rule
Approximate area using trapezia.