What is Migration?

Step 1: Definition of integration in calculus. Integration is the inverse process of differentiation. It finds the antiderivative (indefinite integral) or the accumulated quantity like area (definite integral) of a function. Indefinite integral: f(x) \, dx = F(x) + C where F'(x) = f(x) and C is the constant of integration. Example: x^2 \, dx = (x^3)/(3) + C Step 2: Definite integral and area under curve. The definite integral from a to b gives the net signed area between the curve y = f(x) and the x-axis: _a^b f(x) \, dx = F(b) - F(a) by the Fundamental Theorem of Calculus. Example: Area under y = x from 0 to 2: _0^2 x \, dx = [ (x^2)/(2) ]_0^2 = (4)/(2) - 0 = 2 Step 3: Notation and uses. f(x) \, dx: indefinite integral. _a^b f(x) \, dx: definite integral. Uses: area, volume, displacement (if v(t) is velocity), total charge (if current), etc. Final answer: Integration is finding f(x) \, dx, the antiderivative or accumulated area/quantity. Integration is the inverse of differentiation: f(x)\,dx = F(x) + C where F'(x) = f(x)