Integration allows us to find the area under the curve. Improper integrals let us find this area (if it’s well defined) even when that curve extends to infinity. Knowing whether the area under a graph up to a large, finite value of x is significantly different from the area under the entire graph can help us simplify calculations and avoid approximation errors.
Lecture Video and Notes
Integrating 1/(5x + 2)2 from 1 to Inﬁnity