Use the Fundamental Theorem to determine the value -of b if the area under the graph of f(x)=x^2

step 1 Okay, so this one's kind of fun because I don't think I've actually ever done this question, but

Use the Fundamental Theorem to determine the value -of b if...

Key Concepts

Antiderivative

An antiderivative of a function is another function whose derivative equals the original function. In the process of finding the area under a curve, the antiderivative is determined first and then evaluated at the given limits of integration, which is essential in applying the Fundamental Theorem of Calculus.

Solving Integral Equations

This concept involves setting up an equation with the result of a definite integral equal to a specific value, and then solving that equation for an unknown variable. It requires both the successful integration of the function and subsequent algebraic manipulation to isolate and determine the parameter in question.

Fundamental Theorem of Calculus

This theorem bridges the concepts of differentiation and integration, stating that if a function is continuous over an interval, then its definite integral over that interval can be computed using any of its antiderivatives. It allows one to evaluate areas under curves by using the difference of the antiderivative evaluated at the endpoints of the interval.

Definite Integral

The definite integral of a function over an interval represents the net area between the function's graph and the horizontal axis, taking into account the sign of the area. It is computed as the difference between the values of an antiderivative evaluated at the upper and lower limits of integration.

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