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

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  1. Jun 27, 2016 #1
    The answer here shows the answer as being

    main-qimg-a155679717f734547cfb33eb9ca1c77d.png
    but my limited knowledge of integrals begs me to asks where did the z go?
     
  2. jcsd
  3. Jun 27, 2016 #2

    fresh_42

    Staff: Mentor

    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.
     
  4. Jun 27, 2016 #3

    BiGyElLoWhAt

    User Avatar
    Gold Member

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