A definite integral is a mathematical concept that represents the area under a curve on a graph. It is used to calculate the exact value of a function over a given interval.
An indefinite integral represents a family of functions that have the same derivative, while a definite integral gives a specific numerical value for the area under the curve.
The Riemann sum is a method for approximating the value of a definite integral by dividing the area under the curve into smaller rectangles. As the number of rectangles increases, the Riemann sum becomes closer to the exact value of the definite integral.
Yes, the limits of integration can be changed as long as the interval remains the same. This is known as the change of variables theorem, and it allows for different representations of the same definite integral.
Definite integrals are used in many fields such as physics, engineering, economics, and statistics. They are used to calculate areas, volumes, and other physical quantities that cannot be easily measured. They are also used in optimization problems to find the maximum or minimum value of a function.