Question

The rate at which the world's oil is being consumed in continuously increasing. Suppose the rate of oil consumption (in billions of barrels per year) is given by the function r=f(t), where t is measure in years and t=0 is the start of 2004

(a) Write a definite integral which represents the total quantity of oil used between the start of 2004 and the start of 2009

(b) Suppose . Using a left-hand sum with five subdivisions, find an approximate value for the total quantity of oil used between the start of 2004 and the star of 2009.

(c) Interpret each of the five terms in the sum f

Answer 1

a) \[\int\limits_{2004}^{2009}rdt\]

Answer 2

b) would this be trapezoidal or simpson's rule?

Answer 3

you can scale the limits to 0 to 5 though

Answer 4

b) or would this be \[\sum_{t=0}^{4}f(t)\]

Answer 5

thanks smartcow

Answer 6

yep
and yes that would be it for b) since it wants "left hand sum"

Answer 7

It is the left-hand summation, which is neither. \[S = \sum_{i=1}^n f(x_{i-1})(x_i - x_{i-1})\]

Answer 8

nice like right out of the textbook :)

Answer 9

where \(f(x_{i-1})\) is the value of the function at x and \(x_i-x_{i-1}\) is your step size.

In this case, your step size will be 4/5, which is going to be a pain.

Answer 10

wouldn't the step size be 1 since there are 5 divisions from 0 to 5

Answer 11

Ah yes. It would. Which makes things easier.