What is the integral of 1/2sin(2pi/n)(r^2-z^2) dz

[Guest432]

The answer here shows the answer as being

but my limited knowledge of integrals begs me to asks where did the z go?

 

[fresh_42]

If $F(z)$ is the antiderivative of $f(z)$, i.e. $F'(z) = \frac{d}{dz} F(z) = f(z)$ then $\int_0^R f(z)dz = F(R) - F(0)$.
Since $F(0) = 0$ in your example, only $F(R)$ is left. It is called the fundamental theorem of calculus.

 

[BiGyElLoWhAt]

Well, in definite integrals, you have a constant as the answer, not a function of the variables.