A rocket lifts off the pad at Cape Canaveral.. math help please!!
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A rocket lifts off the pad at Cape Canaveral.. math help please!!

[From: ] [author: ] [Date: 12-02-03] [Hit: ]
and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x is less than or equal to 4000 miles. Find the work, W1, done against gravity when the rocket rises 2000 miles.......
According to Newton's Law of Gravitation, the force of gravity on the rocket is given by F(x)= (-GMm) / (x^2) where M is the mass of the earth, m is the mass of the rocket, G is a universal constant, and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x is less than or equal to 4000 miles. Find the work, W1, done against gravity when the rocket rises 2000 miles. Next, find the limit of the work, W2, as the rocket rises infinitely far from the earth... i really need help on this, i don't even know where to start or how to solve this

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dW = F dx

W = integral F dx

Now that you see where to start, can you do it now? If not, let it be known (be specific so we can understand how to best address your confusion), but I suspect this is all you need.

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Recall integral x^n dx = x^{n+1} / (n+1) , here n = -2. These are all the steps. Please advise.
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