Solution Found!
Infinite intervals of integration Evaluate the
Chapter 7, Problem 17E(choose chapter or problem)
Infinite intervals of integration Evaluate the following integrals or state that they diverge.
\(\int_{0}^{\infty} \frac{x}{\sqrt{x^{4}+1}} d x\)
Questions & Answers
QUESTION:
Infinite intervals of integration Evaluate the following integrals or state that they diverge.
\(\int_{0}^{\infty} \frac{x}{\sqrt{x^{4}+1}} d x\)
ANSWER: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