(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

i)

[tex]\int[/tex][tex]^{\infty}_{}[/tex] (cos x)/(x +exp(x))dx

[tex]_{ 0}[/tex]

ii)

[tex]\int[/tex][tex]^{\infty}_{}[/tex] (x + [tex]\sqrt{x})^{-1}[/tex]dx

[tex]_{ 1}[/tex]

iii)

[tex]\int[/tex][tex]^{\infty}_{}[/tex] (1 + x[tex]^{3}[/tex])[tex]^{-1/2}[/tex]dx

[tex]_{ 1}[/tex]

3. The attempt at a solution

i) x +exp(x) [tex]\geq[/tex] 1

-1[tex]\leq[/tex]cos x [tex]\leq[/tex]1

-1[tex]\leq[/tex](cos x)/(x +exp(x))[tex]\leq[/tex]1/(x +exp(x))

then do i have to compare something to something knowing for certain that something convereges?

For ii) + iii) please can someone nudge me in the right direction.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integral convergence

**Physics Forums | Science Articles, Homework Help, Discussion**