- #1
Dell
- 590
- 0
[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?
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?