Question

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 δ(r) = 50/(1 + r) kg/m2.

a)If the slick extends from ? = 0 to ? = 10,000 m, find a Riemann sum approximating the total mass of oil in the slick.

b) Find the exact value of the mass of oil in the slick by turning your sum into an integral and evaluating it.

c) Within what distance ? is half the oil of the slick contained?

Answer 1