Question

What is the difference between definite integral and indefinite integral?

Answer 1

Hint: In this problem, we have to find the difference between the definite and the indefinite integral. We should know that a definite integral represents a number when the lower and the upper limits are constants, the indefinite integral represents a family of functions whose derivatives are f. The difference between any two functions in the family is a constant. We can now see the difference briefly.

Complete step-by-step answer:
Here we can see the difference between definite and indefinite integral.
We can first see about the indefinite integral.
We should know that a definite integral has limits of integration and the answer is a specific area.
For example, the function \[\int\limits_{1}^{3}{{{x}^{3}}}dx\], where the numbers 3 and 1 are the upper and the lower limits and on integrating it gives a constant as answer.
 We can now see that an indefinite integral can return the function as an independent variable, that is it does not contain any limits over there.
For example, the function \[\int{{{x}^{3}}}dx\], where there are no limits here and the integration answer will be the function itself.

Note: Students should always remember that a definite integral represents a number when the lower and the upper limits are constants, the indefinite integral represents a family of functions whose derivatives are f. A definite integral has limits of integration and the answer is a specific area where an indefinite integral can return the function as an independent variable.