Terms 15

Antiderivative

Function F(x) whose derivative is f(x); basis of indefinite integrals

Indefinite Integral

∫f(x)dx = F(x) + C; general antiderivative with constant C

Definite Integral

∫[a to b] f(x)dx; gives exact area under curve from a to b

Fundamental Theorem of Calculus

∫[a to b] f(x)dx = F(b) − F(a); connects derivatives and integrals

Power Rule (integration)

∫x^n dx = x^(n+1)/(n+1) + C; for n ≠ −1

∫(1/x)dx

ln|x| + C

∫e^x dx

e^x + C

∫sin(x)dx

−cos(x) + C

∫cos(x)dx

sin(x) + C

U-Substitution

Integration technique substituting u = g(x) to simplify complex integrals

Integration by Parts

∫u dv = uv − ∫v du; for products of functions

Riemann Sum

Approximation of integral using sum of rectangle areas

Area Between Curves

∫[a to b] [f(x) − g(x)]dx where f(x) ≥ g(x)

Improper Integral

Integral with infinite limits or discontinuous integrand; use limits

Average Value

f_avg = (1/(b−a)) × ∫[a to b] f(x)dx

Calculus — Integrals