An integral is a mathematical concept that represents the area under a curve in a graph. It is used to find the total value of a function over a given interval.
The purpose of evaluating an integral is to find the exact numerical value of the area under a curve, which can be useful in various real-world applications such as calculating the total distance traveled or the total amount of work done.
There are several methods for evaluating an integral, including the fundamental theorem of calculus, substitution, integration by parts, and trigonometric substitution. The appropriate method to use depends on the complexity of the function and the specific problem at hand.
A definite integral has specific limits of integration and represents the exact numerical value of the area under the curve. An indefinite integral does not have limits of integration and represents a family of functions that differ only by a constant value.
Integrals are commonly used in physics to calculate work, force, and displacement. They are also used in chemistry to calculate reaction rates and concentrations. In biology, integrals are used to model population growth and in medicine, they are used to calculate drug dosages and blood flow.