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Definite Integral

Definition

A definite integral is a mathematical tool used to calculate the exact area between a function and the x-axis over a specific interval.

Analogy

Imagine you have a garden bed with irregular shapes, and you want to know the exact area of each shape. By using a measuring tape and carefully calculating the area within each boundary, you can find the definite integral for that particular garden bed.

Related terms

Indefinite Integral: An indefinite integral represents an antiderivative of a function without specifying any bounds. It gives us a family of functions that differ only by a constant.

Fundamental Theorem of Calculus: The fundamental theorem of calculus establishes the relationship between differentiation and integration. It states that if we differentiate an antiderivative, we obtain the original function.

Area Under Curve: The area under curve refers to the total area enclosed by a curve on a graph. In calculus, it often involves finding definite integrals to determine this area accurately.