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Please help me find my mistake in this integration

  • Thread starter Dell
  • Start date
  • #1
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[tex]\int[/tex]dx/x*(x2-1)0.5 (from 1 to infinity)

i said t=(x2-1)0.5, therefore x2=t2+1
dt=x/(x2-1)0.5

so now i have

[tex]\int[/tex]dx/x*(x2-1)0.5=[tex]\int[/tex]xdx/x2*(x2-1)0.5=[tex]\int[/tex]dt/x2=[tex]\int[/tex]dt/t+1 (now integral from 0 to infinity)

[tex]\int[/tex]dt/t+1 (from 0 to infinity)

=lim arctan(t)[tex]^{b}_{0}[/tex]=pi/4
b-inf


but the correct answer is pi/2, can ANYONE see where i have gone wrong?
 

Answers and Replies

  • #2
Cyosis
Homework Helper
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You didn't adjust your limits after the substitution. If [itex]t=\sqrt{x^2-1}[/itex] and x goes from 1 to infinity then t goes from 0 to infinity.

ps. It would be nice if you use brackets properly so we don't have to guess which function is actually being integrated.
 
  • #3
590
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if you look at the 5th line of text youll see that i did change my limits,
 
  • #4
Cyosis
Homework Helper
1,495
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I missed that, still are you sure you didn't use the old limits? As they yields pi/4. So what's arctan(0) and what's arctan(x) with x going to infinity? Hint: your mistake has to do with filling in the limits.
 
Last edited:

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