Evaluate the following improper integral whenever it is convergent.
E) the integral is divergent

Question

Evaluate the following improper integral whenever it is convergent. 
E) the integral is divergent

Quizplus · Accepted Answer

The given integral is:
$$\int_0^{\infty} e^{-(\ln t)^2} \ dt$$
Let $u = \ln t$, then $du = \frac{dt}{t}$. Substituting $u$, we get:
$$\int_{-\infty}^{\infty} e^{-u^2} \ du$$
This is a known integral, equal to $\sqrt{\pi}$. Hence, the given integral converges and its value is $\sqrt{\pi}$.

The correct answer is (B).

Evaluate the Following Improper Integral Whenever It Is Convergent