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Definite integrals
Definite Integrals A definite integral , denoted by the symbol ∫ , is the area under the curve of a function. It represents the total area of the regi...
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Definite Integrals A definite integral , denoted by the symbol ∫ , is the area under the curve of a function. It represents the total area of the regi...
Definite Integrals
A definite integral, denoted by the symbol ∫, is the area under the curve of a function. It represents the total area of the region bounded by the curve and the x-axis.
To evaluate a definite integral, we use a technique called antiderivative.
An antiderivative, denoted by the symbol ∫f(x)dx, represents a function whose derivative is f(x). By evaluating the antiderivative, we can find the area under the curve of a function.
Examples:
Evaluating the definite integral of f(x) = x^2 from x = 0 to x = 1 is 1/3. This is the area of the parabola with the equation y = x^2 between x = 0 and x = 1.
Evaluating the definite integral of f(x) = 1/x from x = 2 to x = 4 is 2. This is the area of the semicircle with the equation y = x^2/4 between x = 2 and x = 4.
Evaluating the definite integral of f(x) = 3x - 1 from x = 1 to x = 2 is 5. This is the area of the triangle with the base and height formed by the curve and the x-axis between x = 1 and x = 2