Integration Basics Flashcards

Grade 12 · Math · Flashcards

Review all key integration formulas, theorems, and techniques for Grade 12 calculus.

Flashcards

∫ c dx: cx + C
∫ xⁿ dx (n ≠ -1): xⁿ⁺¹/(n+1) + C
∫ eˣ dx: eˣ + C
∫ aˣ dx: aˣ/ln(a) + C
∫ sin x dx: -cos x + C
∫ cos x dx: sin x + C
∫ sec²x dx: tan x + C
∫ 1/x dx: ln|x| + C
FTC Part 1: If F(x) = ∫ₐˣ f(t)dt, then F'(x) = f(x)
FTC Part 2: ∫ₐᵇ f(x)dx = F(b) - F(a)
U-Substitution: Replace u = g(x), du = g'(x)dx to simplify ∫f(g(x))g'(x)dx into ∫f(u)du
Properties of Definite Integrals: ∫ₐᵃ f dx = 0; ∫ₐᵇ f dx = -∫ᵦₐ f dx; ∫ₐᵇ(f+g)dx = ∫ₐᵇ f dx + ∫ₐᵇ g dx
Average Value of a Function: f_avg = (1/(b-a)) · ∫ₐᵇ f(x) dx
Area Between Two Curves: ∫ₐᵇ [top(x) - bottom(x)] dx, where top(x) ≥ bottom(x) on [a,b]