Use the Fundamental Theorem to find the area under f(x)=x^2...

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Key Concepts

Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus connects the concept of differentiation with that of integration. It states that if a function is continuous on a closed interval, then its definite integral over that interval can be computed using any of its antiderivatives by evaluating the difference between the values of the antiderivative at the endpoints.

Antiderivative

An antiderivative of a function is another function whose derivative is the original function. When calculating definite integrals, finding an antiderivative allows us to use the Fundamental Theorem of Calculus by evaluating the antiderivative at the interval's boundaries.

Definite Integral

A definite integral represents the net accumulation of a quantity, often thought of as the net area under a curve between two points on the x-axis. By applying the Fundamental Theorem of Calculus, the definite integral can be computed using the values of an antiderivative at the limits of integration.

Area Under a Curve

The area under a curve between two points on the x-axis is determined by the definite integral of the function over that interval. This concept is crucial in understanding how integration summarizes the accumulation of quantities and measures space under a graph.

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