What are integrals and how do they work?

What are integrals and how do they work?

Integrals are a fundamental concept in calculus that represent the area under a curve. They can be used to calculate things like total distance, area, and volume.

Can you explain the difference between definite and indefinite integrals?

Sure! A definite integral has specific limits and gives a numerical value representing the area under the curve between those limits. An indefinite integral, on the other hand, represents a family of functions and includes a constant of integration.

How do you calculate a definite integral?

To calculate a definite integral, you first find the antiderivative of the function, then evaluate it at the upper and lower limits and subtract the two results.

Can you give me an example of a definite integral?

Of course! For example, to calculate the definite integral of f(x) = x^2 from 1 to 3, you would find the antiderivative, which is (1/3)x^3, and then evaluate it at 3 and 1.