Understanding Integrals
Integrals are one of the two main concepts of calculus, with the other being derivatives. The integral can be thought of as the area under a curve. It's a way to add up infinitely many things, an essential concept in both pure and applied mathematics.
The Definite and Indefinite Integral
The definite integral is used to calculate the total of a range of numbers and is denoted by the following integral sign, a = lower limit and b = upper limit:
$$ \int_a^b f(x) \, dx $$
The indefinite integral, on the other hand, is a function that describes the antiderivative, with no set limits:
$$ \int f(x) \, dx = F(x) + C $$