What is integration in calculus?
Answer
Integration is the process of finding a function whose derivative is given, and geometrically it represents the area under a curve.
The working
Inverse of differentiation
Integration is the reverse operation of differentiation, so it is also called anti-differentiation; ∫f(x)dx gives a function whose derivative is f(x).
Indefinite integral
An indefinite integral, ∫f(x)dx = F(x) + C, includes an arbitrary constant C because differentiation of any constant gives zero.
Definite integral
A definite integral ∫ from a to b of f(x)dx gives a definite number equal to the area under the curve between x = a and x = b.
Uses
Integration is used to find areas, volumes, lengths of curves, and accumulated quantities like displacement from velocity.
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