Mathematics - Calculus - Integral - Definite integrals and area - Evaluating Definite Integrals

8 steps: (1) ∫[a,b] f(x)dx = F(b) - F(a) where F'=f. (2) Example: ∫[1,3] x²dx = [x³/3]₁³ = 27/3 - 1/3 = 26/3. (3) Area between curve and x-axis: split at zeros if function changes sign. (4) Area between TWO curves: ∫[a,b] [top(x) - bottom(x)]dx. (5) Example: area between y=x² and y=x from 0 to 1. ∫[