Evaluating a Definite Integral - Example 1/(9+x^2)

In this video we evaluate the definite integral of 1/(9+x²) from x=0 to x=3. An function must be continuous over the domain of integration for a definite integral to work. Definite integrals always result in a number or a value, rather than an anti-derivative function (as in the case of indefinite integrals).

Firstly, we can rewrite the integrand as:

\frac{1}{3^2+x^2}

The anti-derivative of this integrand is:

\frac{1}{3}\arctan \left ( \frac{x}{3} \right )

For definite integrals, we don't need to include the integration constant "+C", because it will cancel itself out when we evaluate the numerical values.

We still need to apply the bounds of the upper limit of x=3 to the lower limit of x=0.

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