Question

What is the difference between definite and indefinite integral?

Answer 1

In definite integral we know that we are given upper and lower limits so after integrating the given function we just get a number and on the other side while doing indefinite integral we just integrate a function and add an arbitrary constant.

Complete step-by-step answer:
Difference between the definite and indefinite integral solution is that in definite integral we know that we are given upper and lower limits so after integrating the given function we just get a number and on the other side while doing indefinite integral we just integrate a function and add an arbitrary constant. Using initial conditions, we can get the value of that arbitrary constant and hence a proper function.
The difference between both of them is of a constant only. When the limits are constant then we get constant value as mentioned above and in hint and if the limits are not constant then we get the function as we get in indefinite integral but without arbitrary constant. We can also say like this, that in a definite integral we just get a number after limits so we can say definite but in indefinite integral since we do not have any upper and lower limits so we don’t get any definite number in our solution and hence get the variables therefore, we can say that it is an indefinite integral and without any given conditions we cannot get the value of arbitrary constant also.

Note: Just remember that we are given the limits in definite integral. Also, we must make sure that we are not getting confused as to how to put the limits and then solve it further or in an indefinite integral how to find the value of the arbitrary constant if asked.