Definite Integrals & Riemann Sum? I'm in Calculus II.

[dartgun]

The exxon Valdez oil spill occured in Prince William Sound, Alaska on March 24th, 1989 when Exxon Valdez, and oil tanker bound for Long Beach, California struck Prince William Sound's Bligh Reef and spilled 260,000 to 750,000 barrels (41,000 to 119,000 m^3) of crude oil. The density of oil in a CIRCULAR oil slick on the surface of the ocean at a distance r meters from the center of the slick is given by p(r) = (50) / (1 + r) kg/m^2.

a.) If the slick extends from r = 0 to r = 10,000 m, find a Riemann sum approximating the total mass of oil in the slick.
b.) Find the EXACT value of the total mass of oil in the slick by turning your sum in part a. into a definite integral and evaluating it. (Integrate by substitution! Not by calculator!)
c.) Within what distance r is half the oil of the slick contained?

 

[Deleted member 4993]

The exxon Valdez oil spill occured in Prince William Sound, Alaska on March 24th, 1989 when Exxon Valdez, and oil tanker bound for Long Beach, California struck Prince William Sound's Bligh Reef and spilled 260,000 to 750,000 barrels (41,000 to 119,000 m^3) of crude oil. The density of oil in a CIRCULAR oil slick on the surface of the ocean at a distance r meters from the center of the slick is given by p(r) = (50) / (1 + r) kg/m^2.

a.) If the slick extends from r = 0 to r = 10,000 m, find a Riemann sum approximating the total mass of oil in the slick.
b.) Find the EXACT value of the total mass of oil in the slick by turning your sum in part a. into a definite integral and evaluating it. (Integrate by substitution! Not by calculator!)
c.) Within what distance r is half the oil of the slick contained?

Since you are in CalcII - you should be able at least start with derivation of the differential. What is it?

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