Calculus 2: Integrals

Indefinite Integral

∫f(x)dx = F(x) + C, where F'(x) = f(x); antiderivative

Definite Integral

∫ₐᵇ f(x)dx = F(b) - F(a); net area under curve from a to b

Fundamental Theorem of Calculus (Part 1)

d/dx [∫ₐˣ f(t)dt] = f(x)

Fundamental Theorem of Calculus (Part 2)

∫ₐᵇ f(x)dx = F(b) - F(a), where F is any antiderivative of f

∫ xⁿ dx

xⁿ⁺¹/(n+1) + C, for n ≠ -1

∫ 1/x dx

ln|x| + C

∫ eˣ dx

eˣ + C

∫ sin x dx

-cos x + C

∫ cos x dx

sin x + C

∫ sec²x dx

tan x + C