∫
Integral Symbol (∫)
The integral symbol (∫) is a central operator in calculus, representing either the area under a curve or the anti-differentiation of a function.
Calculus Definition & Usage
Sum of Infinitesimal Areas
The integral symbol is derived from an elongated 'S', signifying 'summation'. A definite integral has lower and upper limits (representing interval bounds) and computes the exact signed area locked between the function curve and the x-axis.
Example Formula
The definite integral of $x^2$ on the interval $[a, b]$ is formulated as:
\int_{a}^{b} x^2 \, dx = \left[ \frac{x^3}{3} \right]_{a}^{b}