Improper Integrals

What:

Sometimes we want to get the area under a curve of integrals where the integrand is discontinuous or unbounded.

How?

We substitute a variable into the integrand and solve the limit of that variable:

If ${\int }_a^{t}f(x)dx$ exists for all $t>a$, we define

$${\int }_a^{\infty }f(x)dx=\underset{t\to \infty }{\lim }{\int }_a^{t}f(x)dx,$$ $${\int }_{-\infty }^{\infty }f(x)dx={\int }_{-\infty }^{a}f(x)dx+{\int }_a^{\infty }f(x)dx.$$