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## Homework Statement

Let's definite the function f(x)=∫（from x to x+1）sin(t^2)dt

## Homework Equations

There is another function of x:

g(x)=cos(x^2)/2x-cos((x+1)^2)/2(x+1)

## The Attempt at a Solution

Prove that when x→+∞，there is the equation:

f(x)=g(x)+O(1/(x^2))

Here the O(u) means that when u→0, the O(u) is at least infinite small comparable to the infinite small quantity u.

I am only a 12 grade highschool student, so I have no methods to solve this. I will be grateful if you could give me some advice. This is a problem from the exercises of the Mathematical Analysis by V.A.Zorich, chapter 6, Volume I.

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