[Math] Difference between integral, anti-derivative, and definite integral

calculusintegration

I'm just starting to learn about anti-derivative (which is basically function F whose derivative is equal to the original function f).

What I want to know is that, is anti-derivative and integral the same thing?

And if so, what is a definite integral? My textbook doesn't go into definite integrals, right know we are dealing with indefinite integrals. What does this mean?

Please don't get too mathy in the explanation

Best Answer

The indefinite integral is the set of antiderivatives (hence the important $+C$ for intervals) and the definite integral is accumulation - equal to the area under the curve $y=f(x)$ if $f \geq 0$. Bottom line:

antiderivative --- one function

indefinite integral --- set of functions

definite integral --- number.

As mentioned in a comment, antiderivatives and definite integrals are related by (a version of) the Fundamental Theorem of Calculus.

Related Question