Using calculus to find gravity in space (dynamics)

[Veirian]

I am currently solving a problem where I need to find the gravity in the ISS (distance 400km from Earth with Radius 6371km). I am using the formula g=GM/R^2 . One way to solve it would be to find GM by multiplying g(which is 9.81) and R^2 (which is known) and then to use it in GM/(R+400)^2 and get 8.7m/s^2.

I was wondering whether there was a way to use calculus to get this. If I integrate with respect to the distance (From 6371 to 6371+400) I get something around -1.02. Does that mean that the value changes from R to R+400 by -1.02 ?
I am having some trouble in deciding when and how to use calculus in physics (more specifically dynamics).

 

[ZapperZ]

I don't understand what the difficulty here is, and why you need to use calculus.

Why can't you just plug in the numbers and find g? Is it because you don't know "M", the mass of Earth? This is something you can easily look up. I don't understand why you're making it more difficult than it is.

Zz.