The integral of the function \( \frac{1}{2}\sin\left(\frac{2\pi}{n}\right)(r^2 - z^2) \) with respect to \( z \) simplifies to a constant value due to the application of the fundamental theorem of calculus. In this context, the antiderivative \( F(z) \) is evaluated at the limits of integration, leading to \( F(R) - F(0) \), where \( F(0) = 0 \). Consequently, the result is solely dependent on \( F(R) \), confirming that the variable \( z \) does not appear in the final answer.
PREREQUISITESStudents and professionals in mathematics, particularly those studying calculus, as well as educators looking for clear explanations of integral concepts.