The integral in this exercise converges. Evaluate the integral without using a table.

To evaluate an integral that is known to converge, we typically look for a method of integration that simplifies the equation. For instance, if you have an integral of the form \(\int_0^\infty e^{-x^2} \, dx\), you can utilize substitution or recognize it as a Gaussian integral, leading you to the result of \(\frac{\sqrt{\pi}}{2}\). This process often involves techniques like integration by parts or recognizing patterns that make it easier, such as trigonometric or exponential functions. A common pitfall is overlooking the limits of integration or misusing properties of the functions involved; ensuring careful consideration of convergence and the behavior at boundaries is crucial!