Calculus
Advanced

Fundamental Theorem of Calculus

Connects differentiation and integration.

Formula

∫abf(x) dx=F(b)−F(a)\int_a^b f(x)\,dx = F(b) - F(a)

Variables

FAntiderivative of f
a, bLimits

Example

∫₀² 2x dx = [x²]₀² = 4 − 0 = 4.

Did You Know?

The fundamental theorem of calculus revealed that differentiation and integration are inverse operations — uniting the whole subject.

integralfundamental theorem