Gravitational potential energy! A small confusion

If i find out the work done by gravity in bringing a mass from infinity to a point R from M then that work should turn out to be positive
but when i do the integral in the systematic way as follows i end up with negative answer :-/

Question

Gravitational potential energy! A small confusion

If i find out the work done by gravity in bringing a mass from infinity to a point R from M then that work should turn out to be positive
but when i do the integral in the systematic way as follows i end up with negative answer :-/

anonymous · Answer

So here goes

|dw:1366988967776:dw|

Since the displacement is downwards and the force of gravity is ALSO downwards.. the work is positive and hence

$$dw= +Fdx$$

hence$$w = \int\limits_{\infty}^{R}{\frac{GMm}{x^2}dx}$$

that yeilds $$w = -\frac{GmM}{R}$$

so what is wrong in this?!?