#6.13 Evaluating Improper Integrals

Remember earlier in this unit when you had to evaluate definite integrals? Now, imagine trying to solve a definite integral with one of the boundaries, instead of being an integer, being to infinity. How would you go about doing that? Today, we’ll learn about improper integrals and how to deal with these cases. 🚀

#🟥 Recap: Definite Integrals

When coming across integration problems, you will encounter one of the following: an indefinite integral or a definite integral. Unlike indefinite integrals, which do not have boundaries, definite integrals have an upper and lower bound that can be plugged into your antiderivative to get a numerical value. Here are some examples of typical definite integrals you may have encountered in AP Calculus AB:

$$∫^π_0sin(x)dx=-cos(π)+cos(0)=2$$

$$∫^2_0e^{-x}dx=-e^{-2}+e^0=-\frac{1}{e^2}+1$$

#♾️ Evaluating Improper Integrals

An improper integral occurs when the limits of integration involve infinity or when the function being integrated becomes unbounded within the integration interval. This basically means that in the interval being evaluated, the function becomes unbounded to infinity.

In order to pro...