joeblow said:
An integral is a mathematical concept that represents the area under a curve in a graph. It is a fundamental tool in calculus and is used to solve many real-world problems.
To evaluate an integral, you need to use the fundamental theorem of calculus, which states that the integral of a function can be calculated by finding the antiderivative of that function and evaluating it at the upper and lower bounds of the integral. This can be done using various techniques such as substitution, integration by parts, or partial fraction decomposition.
The limits of integration are the upper and lower bounds of the integral, which define the range over which the function is being integrated. These limits can be constants, variables, or expressions.
Evaluating integrals is important because it allows us to find exact solutions to real-world problems that involve continuous change. It is also a vital tool in many branches of mathematics and physics, such as calculating areas, volumes, and probabilities.
A definite integral has specific upper and lower bounds, while an indefinite integral does not. A definite integral represents a single numerical value, while an indefinite integral represents a family of functions that differ by a constant. In other words, a definite integral gives a specific answer, while an indefinite integral gives a general solution.
