- #1

- 590

- 0

^{2}-1)

^{0.5}(from 1 to infinity)

i said t=(x

^{2}-1)

^{0.5}, therefore x

^{2}=t

^{2}+1

dt=x/(x

^{2}-1)

^{0.5}

so now i have

[tex]\int[/tex]dx/x*(x

^{2}-1)

^{0.5}=[tex]\int[/tex]xdx/x

^{2}*(x

^{2}-1)

^{0.5}=[tex]\int[/tex]dt/x

^{2}=[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?