Math basics › Calculus
Integrals
Undoing a derivative
∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C, for n ≠ −1. Add one, divide by the new power.
Do not lose the + C
An indefinite integral is a whole family of functions. The constant is part of the answer.
Definite integrals are area
∫ from a to b is the signed area between the curve and the x-axis. Below the axis counts as negative.
The fundamental theorem
∫ from a to b of f = F(b) − F(a), where F′ = f. It is why antiderivatives compute areas at all.