Question

What does integration mean?

Answer 1

Meaning of Integration.

If a function $f$ is differentiable in an interval $\mathrm{I}$, i.e. its derivative $f\text{'}$exists at each point of I, then a natural question arises given $f\text{'}$at each point of interval $\mathrm{I}$, Can we determine the function? The functions that could possibly have given function as a derivative are called antiderivatives (or primitive) of the function. Further, the formula that gives all these antiderivatives is called the integral of the function, and such a process of finding antiderivatives is called integration.

Integration is also helpful in finding the volumes, Area, Displacement, etc. Integration is one of the two major subtopics of calculus apart from differentiation. In differentiation, we study the rate of change of the function with respect to the variable.

There are two types of integration:

• Definite integrals: Any integral that contains both the upper and lower limits.
• Indefinite integrals: Any integral that does not contains upper and lower limits.

Thus, The formula that gives antiderivatives of a function $f\text{'}$ is called the integral of the function, and such a process of finding antiderivatives is called integration. Where $f\text{'}$ is derivative of $f$ in some interval $\mathrm{I}$