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A definite integral is a mathematical concept used to find the area under a curve between two specific points on a graph. It is represented by the symbol ∫ and has a lower and upper limit of integration.
To evaluate a definite integral, you need to first find the indefinite integral of the function. Then, you substitute the upper and lower limits of integration into the indefinite integral and find the difference between them to get the value of the definite integral.
A definite integral has specific limits of integration and gives a numerical value, while an indefinite integral has no limits and gives a general formula that represents a family of functions.
Evaluating definite integrals is important in many fields, including physics, engineering, and economics. It allows us to find the area under a curve, which can represent quantities such as displacement, velocity, or profit. It also helps us solve problems involving motion, optimization, and probability.
Some common techniques for evaluating definite integrals include substitution, integration by parts, partial fractions, and trigonometric substitution. The choice of technique depends on the complexity of the integral and the form of the function being integrated.