Infinite intervals of integration Evaluate the following integrals or state that they diverge.

Problem 17E

Infinite intervals of integration

Evaluate the following integrals or state that they diverge.

Solution:

Step 1

To evaluate the following integral, we use method of integration by substitution.

We substitute

Squaring both sides, we get

Differentiating , we get

Arranging I as follows so that we can substitute.

Substituting these values in the integral , we get

Changing the variables to the original, we get