$$\int$$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

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

$$\int$$dt/t+1 (from 0 to infinity)

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

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

Cyosis
Homework Helper
You didn't adjust your limits after the substitution. If $t=\sqrt{x^2-1}$ 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.

if you look at the 5th line of text youll see that i did change my limits,

Cyosis
Homework Helper
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: