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

• B
The answer here shows the answer as being

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

## Answers and Replies

fresh_42
Mentor
2021 Award
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
Gold Member
Well, in definite integrals, you have a constant as the answer, not a function of the variables.