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Calculus Level 4

Let \(l\) be the secant line connecting the points on the graph of \(f(x)=x^2\) when \(x=n\) and \(x=n+1.\) The positive value of \(k\) that makes the following expression always true can be represented as \(\frac{A}{B},\) for positive coprime \(A\) and \(B.\) Find \(A+B.\) \[\int_n^{n+k}f(x)\text{ }dx=\int_n^{n+k}l\text{ }dx\]

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