# Calculus

posted by
**Jane** on
.

assume the rate at which the world's oil is being consumed is

r = 27 e^0.06 t.

Here, just as in your book, r is in billions of barrels per year, t is in years, and t = 0 is January 1, 1990.

(a) Fill in the blanks below to express the definite integral which measures the total quantity of oil used between the start of 1990 and the start of 1996:

∫ab dt,

where a = and b = .

(b) Use the Fundamental Theorem of Calculus to evaluate the integral.

Answer: billion barrels.