Question:
Evaluate the following integral using Gamma function.
Integrate x from 0-->1 dx/((-ln(x))^(1/2))
My approach:
I let -ln(x) = u ==> ln(x) = -u ==> x = e^(-u)
==> dx = -(e^(-u))
Limits of u: 0-infinty, which gives,
Integrate u from 0-->1 dx/((-ln(x))^(1/2)) = Integrate u from 0-->infinity { - du/((u^(1/2))*(e^(-u))) }
= -Gamma function[ (-1/2) + 1 ] = -(-1/2) * Gamma function [ (-1/2) ]
= (1/2) * (-2 * sqrt(pi) )
= -sqrt(pi)
Is this approach correct?
Thank you in advance!
looks good, but I get √π
did you lose track of the sign somewhere?