Calc 2 Homework Integral Problem

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So I have this homework problem : "A radiation detector is a circular disk which registers photons which hit it. The probability that a photon hitting the disk at a distance r from the center is actually detected is given by S(r). A radiation detector of radius R is bombarded by constant radiation of N photons per second per unit of area. Write an integral representing the number of photons per second registered by the detector."

It would help if someone made English of this for me haha. I was thinking maybe the integral from a-b of S(r)*N dr? Let me know of any suggestions or answers or any help really, thanks!
 

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