Question

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Answer 1

Answer:

The integral diverges

Step-by-step explanation:

Consider the integral from 0 to infinity of

$xe^{4x}$

We can do this in parts

$\int {xe^{4x} } \, dx =\int {x} \, d(e^{4x})/4\\ = x/4 e^{4x}-e^{4x}/16$

When we substitute limits infinity we find that the values become infinity

Hence the integral diverges

The given improper integral diverges