Answer:
the total amount of water supplier per hour to the region within a circle of radius R=110 ( that is from distance r, 0<r<110)
[tex]W(R) = 2\pi [1-(R+1)e^{-R}][/tex]
Step-by-step explanation:
if f(r) describes the water supplied at a distance r , the total amount supplied inside a region that goes from 0 until the circle of radius R, is the sum of all f(r) values from 0 until R, that is the integral value over these limits.
The formula deduction can be found in the attached picture
There is an "r" that multiplies e^-r as result of changing from rectangular coordinates to polar ones.(dx*dy --> r*dr*da)
