Use a definite integral to find the area of the region between the given curve and the x -axis o

step 1 Okay, what we want to do is we want to use a definite integral to find the area that is bounded

Use a definite integral to find the area of the region...

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Key Concepts

Definite Integral

A definite integral computes the accumulation of quantities, such as areas or total change, over a specific interval. In calculus, it is used to find the area under a curve between two boundaries along the x-axis by integrating the function that defines the curve.

Area Under a Curve

The concept of area under a curve involves calculating the region enclosed by the function and the x-axis. This is achieved by setting up and evaluating a definite integral where the lower and upper limits correspond to the interval over which the area is computed.

Antiderivative

An antiderivative of a function is another function whose derivative is the original function. Finding an antiderivative is a key step in evaluating a definite integral, according to the Fundamental Theorem of Calculus.

Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus links differentiation and integration, stating that the definite integral of a function over an interval can be computed using any of its antiderivatives evaluated at the endpoints of that interval. This theorem provides the foundation for evaluating areas and accumulated quantities in calculus.

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