[top] — Integrals -zambak-

Elias gasped, stumbling back into his chair. The book slammed shut in front of him.

✔ Indefinite integral = family of antiderivatives ✔ Definite integral = limit of Riemann sums ✔ FTC links differentiation and integration ✔ Master substitution, by-parts, partial fractions ✔ Apply to area, volume, work, average value Integrals -Zambak-

| Type | Formula | |------|---------| | Power Rule | ( \int x^n dx = \fracx^n+1n+1 + C \ (n \neq -1) ) | | Natural Log | ( \int \frac1x dx = \ln |x| + C ) | | Exponential | ( \int e^x dx = e^x + C ) | | Sine | ( \int \sin x dx = -\cos x + C ) | | Cosine | ( \int \cos x dx = \sin x + C ) | | Substitution | ( \int f(g(x)) g'(x) dx = \int f(u) du ) | | FTC | ( \int_a^b f(x) dx = F(b)-F(a) ) | | Area | ( \int_a^b [f(x)-g(x)] dx ) | Elias gasped, stumbling back into his chair