To evaluate the integral , we first find the antiderivative of , which is . Now, we can compute the definite integral:

There you go, the value of the integral is .

Now, let’s explore some fun facts about this integral!

First, did you know that higher-degree polynomial integrals like this are frequently used in physics? For example, calculating the area under curves can help determine the work done by a force over a distance or the center of mass of irregular shapes!

Additionally, when performing numerical integration, common mistakes tend to include miscalculating the bounds of integration or using the wrong function for evaluation. So always double-check that the function symmetry or other properties don’t make your calculations easier!