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 represents the accumulation of quantities, which can be interpreted geometrically as the area under a curve between two points on the x-axis. It is computed by finding the antiderivative of the function and then evaluating it at the endpoints of the interval, resulting in the net area between the function and the x-axis.

Area Under a Curve

The area under a curve refers to the region bounded by the curve, the x-axis, and vertical lines at given endpoints. When the function is non-negative over the interval, the definite integral directly gives the physical area of that region.

Fundamental Theorem of Calculus

This theorem connects differentiation and integration by stating that if a function is continuous over an interval, then its definite integral can be computed using any of its antiderivatives; the difference of the antiderivative evaluated at the endpoints yields the value of the integral.

Power Rule for Integration

The power rule for integration is a method used to integrate polynomial functions. It states that the integral of x raised to a power n (where n ? -1) is x raised to the power n+1 divided by n+1, plus a constant of integration for indefinite integrals, and is used to evaluate the definite integral for functions like x².

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