An integral is a mathematical concept that represents the area under a curve in a graph. It is also known as the antiderivative or the primitive function.
Determining the integral is important because it allows us to find the total amount of a quantity, such as distance or volume, from a given rate of change. It also helps in solving various real-world problems in physics, economics, and other fields.
The process of determining the integral is called integration. It involves finding the antiderivative of a function, which is the original function before taking the derivative. Integration can be done using various techniques such as substitution, integration by parts, and partial fractions.
A definite integral has specific upper and lower limits and gives a numerical value, while an indefinite integral does not have limits and gives an equation with a constant term. Definite integrals are used to find the total amount of a quantity, while indefinite integrals are used to find the general solution to a differential equation.
Determining integrals has various applications in different fields such as physics, engineering, economics, and statistics. It is used to find the area under a curve, the volume of a solid, the work done by a variable force, the velocity of an object, and the probability of an event. It is also used in optimization problems to find the maximum or minimum value of a function.