Video Transcript
Is the integral between zero and ∞ of 𝑒 to the negative 𝑥 squared power with respect to 𝑥 an improper integral?
Let’s start by reminding ourselves how we check whether an integral is improper. One way to check whether an integral is improper is to check whether one or both of the limits of integration are ∞. That’s integrals of the form the integral between 𝑎 and ∞ of 𝑓 of 𝑥 with respect to 𝑥 where 𝑎 is any real number, or the integral between negative ∞ and 𝑎 of 𝑓 of 𝑥 with respect to 𝑥, or integrals of the form the integral between negative ∞ and ∞ of 𝑓 of 𝑥 with respect to 𝑥.
We can see that this integral is of this form where the upper limit is ∞. So, yes, this integral is classed as an improper integral.
