Math2.org Math Tables: Integral Identities

(Math)

Formal Integral Definition:
when...

a = x0 < x1 < x2 < ... < xn = b
d = max (x1-x0, x2-x1, ... , xn - x(n-1))
xk-1 <= Xk <= xk     k = 1, 2, ... , n
F '(x) dx = F(b) - F(a) (Fundamental Theorem for integrals of derivatives)
a f(x) dx = a f(x) dx (if a is constant)

f(x) + g(x) dx = f(x) dx + g(x) dx

$\int_a^b f(x) dx = \left[ \int f(x) \, dx \right]_a^b$

f(x) dx + f(x) dx = f(x) dx

(integration by substitution)