Oil well burning in a 100 miles of the well

Question

When an oil well burns, sediment is carried up into the air by the flames and is eventually deposited on the ground. Less sediment is deposited further away from the well. Experimental evidence indicates that the density (in tons per square mile) at a distance r in any direction from the burning oil well is given by the formula S(r) = (7/(1+r^2)). In order to estimate how large a clean up crew to hire, a company must estimate how many tons of sediment must be removed within 100 miles of the well. Find and evaluate the integral that represents this total deposit.

Answer 1

Need to add up all the deposits for all distances from 0 to 100 miles from the oil well.

Total tons = ∫₀¹⁰⁰7/(1+r²) dr = 7 tan^-1(r)|₀¹⁰⁰ =10.93 tons