Evaluating a Definite Integral In Exercises 57-64 , evaluate...

Evaluating a Definite Integral In Exercises $57-64$ , evaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result.
$$
\int_{0}^{8} \frac{2 x}{\sqrt{x^{2}+36}} d x
$$

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Key Concepts

Graphing Utilities for Verification

Graphing calculators or software are useful tools for confirming the results of an integral by both plotting the function and computing numerical approximations, thus providing a practical check against the analytical solution.

Fundamental Theorem of Calculus

This theorem connects differentiation and integration, stating that if a function is continuous over an interval, its definite integral can be evaluated by finding an antiderivative, and then computing the difference of this antiderivative at the endpoints of the interval.

u-Substitution (Change of Variables)

u-Substitution is a method used to simplify integrals by replacing a composite part of the integrand with a single variable 'u'. This technique transforms the integral into a more manageable form that often directly reveals the antiderivative.

Definite Integral

A definite integral calculates the net area under a curve between two specified boundaries. It is found by evaluating the antiderivative of the integrand at the upper and lower limits and then taking the difference, as per the Fundamental Theorem of Calculus.

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