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What is #f(x) = int x-xsec(x/2) dx# if #f((7pi)/4) = 0 #?

Answer 1

Because the indefinite integral involves the imaginary valued polylogarithmic function, I believe that there is an error in the question.

Wolfram Alpha gives the solution to the indefinite integral as

#4i(Li_2(-ie^((ix)/2)) - Li_2(ie^((ix)/2))) +x^2/2-2x(ln(1-ie^((ix)/2)) - ln(1+ie^((ix)/2))) +C#

Now substitute #(7pi)/4# for #x#, set equal to #0# and solve for #C#.

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Answer 2

Axel Alvarez

The function ( f(x) = \int (x - x\sec(\frac{x}{2})) , dx ) is undefined without specified limits of integration. Therefore, it is not possible to determine the function without further clarification.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.