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.