anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
a) \[\int\limits_{2004}^{2009}rdt\]
anonymous
  • anonymous
b) would this be trapezoidal or simpson's rule?
dumbcow
  • dumbcow
you can scale the limits to 0 to 5 though

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anonymous
  • anonymous
b) or would this be \[\sum_{t=0}^{4}f(t)\]
anonymous
  • anonymous
thanks smartcow
dumbcow
  • dumbcow
yep and yes that would be it for b) since it wants "left hand sum"
anonymous
  • anonymous
It is the left-hand summation, which is neither. \[S = \sum_{i=1}^n f(x_{i-1})(x_i - x_{i-1})\]
dumbcow
  • dumbcow
nice like right out of the textbook :)
anonymous
  • anonymous
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.
dumbcow
  • dumbcow
wouldn't the step size be 1 since there are 5 divisions from 0 to 5
anonymous
  • anonymous
Ah yes. It would. Which makes things easier.

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