An integral is a mathematical concept that represents the area under a curve. It is used to calculate the total value of a continuous function within a given interval.
Integrals are useful in many areas of science, particularly in physics and engineering. They allow us to calculate important values such as total distance traveled, total force applied, and total energy used.
A definite integral has specific upper and lower limits, and gives a numerical value as the answer. An indefinite integral has no limits and gives a function as the answer.
The process for solving an integral depends on the type of integral and the function being integrated. Some methods include substitution, integration by parts, and using special rules such as the power rule or trigonometric identities.
The fundamental theorem of calculus states that differentiation and integration are inverse operations. In other words, the derivative of an integral is equal to the original function, and the integral of a derivative is equal to the original function plus a constant.