Math Indefinite integrals Integrate vs. differentiate

Integrate vs. differentiate

Integration is the opposite operation of differentiation.

differentiation and integration

By integrating a derivative $f'(x)$ one obtains $f(x)$ and integrating again $F(x)$.
The integration can be reversed with differentiation.



Overall difference between differential and integral calculus:

  • Differential calculation: Calculation of the derivative of a antiderivative
    => differentiate

  • Integral calculus: Calculation of the antiderivative of the derivative
    => integrate