n∫ⁿ f(x)dx
The notation n∫ⁿ f(x)dx represents the definite integral of the function f(x) with respect to x, where the variable of integration is x and the lower limit of integration is n
The notation n∫ⁿ f(x)dx represents the definite integral of the function f(x) with respect to x, where the variable of integration is x and the lower limit of integration is n.
To compute this definite integral, you can use the fundamental theorem of calculus. The fundamental theorem of calculus states that if F(x) is an antiderivative of f(x), then the definite integral of f(x) from a to b is equal to F(b) – F(a).
In this case, assuming that f(x) is a well-behaved function that has an antiderivative, you can find an antiderivative F(x) of f(x). Then, you can evaluate F(x) at the upper limit of integration, n, and subtract the value of F(x) at the lower limit of integration, also n.
The result of evaluating n∫ⁿ f(x)dx would be F(n) – F(n). However, since the upper and lower limits of integration are the same (n), the integral evaluates to zero.
Therefore, n∫ⁿ f(x)dx = 0 for any function f(x) and any value of n.
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