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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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