This diverges.
Why:
First of all, note that ∫(-∞ to ∞) 2x dx/√(x^2+9)
= ∫(0 to ∞) 2x dx/√(x^2+9) + ∫(0 to ∞) 2x dx/√(x^2+9).
So, this integral converges <==> Both terms converge.
However, ∫(0 to ∞) 2x dx/√(x^2+9) diverges by the Comparison Test,
because 2x/√(x^2+9) < 2x/√(x^2 + 0) = 2 for all x, and ∫(0 to ∞) 2 dx clearly diverges.
Hence, the integral in question diverges.
I hope this helps!
Copyright © 2024 1QUIZZ.COM - All rights reserved.
Answers & Comments
Verified answer
This diverges.
Why:
First of all, note that ∫(-∞ to ∞) 2x dx/√(x^2+9)
= ∫(0 to ∞) 2x dx/√(x^2+9) + ∫(0 to ∞) 2x dx/√(x^2+9).
So, this integral converges <==> Both terms converge.
However, ∫(0 to ∞) 2x dx/√(x^2+9) diverges by the Comparison Test,
because 2x/√(x^2+9) < 2x/√(x^2 + 0) = 2 for all x, and ∫(0 to ∞) 2 dx clearly diverges.
Hence, the integral in question diverges.
I hope this helps!