Question

Medal will be given if shown work and final answer. Determine whether the integral converges or diverges, and if it converges find its value.

Answer 1

\[\int\limits_{4}^{\infty}\frac{ 1 }{ x \sqrt{x} }dx\]

Answer 2

yes ut converges to one

Answer 3

Could someone please explain how they got their answer?

Answer 4

@Hero

Answer 5

@jim_thompson5910
could you help me?

Answer 6

\[\int\limits_{4}^{\infty}\frac{ dx }{ x \sqrt{x} }=\int\limits_{4}^{\infty}x^{-\frac{ 3 }{ 2 }}\,dx=\left[ -2x^{-\frac{ 1 }{ 2 }} \right]_{4}^{\infty}=\lim_{x \rightarrow \infty}-2x^{-\frac{ 1 }{ 2 }} -\left( -2(4)^{-\frac{ 1 }{ 2 }}\right)\]

Answer 7

Thank you so much!

Answer 8

does that make sense?