Integration Formulas and Integral Rules: Complete List
Every basic integration formula and integral rule: power, exponential, log, trig and inverse trig integrals, substitution, by parts and definite integrals.
Every basic integration formula and integral rule: power, exponential, log, trig and inverse trig integrals, substitution, by parts and definite integrals.
Class 12 Integrals: standard formulas, substitution, partial fractions, integration by parts, special integrals and definite integral properties, solved.
What Calc 1 and Calculus 2 cover topic by topic, which is harder, what comes next, and a study plan with free guides and step-by-step calculators.
Area between curves = ∫(top − bottom)dx. Find intersection points, handle curves that cross, and integrate with respect to y when easier. Worked examples.
How to compute left, right and midpoint Riemann sums, the trapezoidal rule and Simpson’s rule, with a full worked example and error comparison.
The average value of f on [a, b] is (1/(b − a))∫f(x)dx. Why the formula works, examples with sin x, x² and eˣ, and the Mean Value Theorem for integrals.
The shell method finds volumes of revolution with V = 2π∫(radius)(height)dx. Step-by-step examples and a clear guide to choosing shells or disks.
Find volumes of solids of revolution with the disk method V = π∫f(x)²dx and the washer method V = π∫(R² − r²)dx. Worked examples and setup tips.
The arc length of y = f(x) from a to b is ∫√(1 + [f'(x)]²) dx. Derivation, worked examples (x^(3/2), a circle, a catenary) and parametric curves.
The Fundamental Theorem of Calculus links derivatives and integrals. Both parts explained with intuition, formulas and worked examples.