Riemann Sums Equation

Question

Management at an oil company estimates that oil will be pumped from a producing field at a rate given by  where the rate of production in thousands of barrels per year years after 2000. Use Riemann Sums with 30 left end rectangles to compute and then interpret the area under between 2002 and 2010.

Answer 1

whatever you come up with should be close to the integral of

200/(t^2+1) +5

evaluated at t= 0 to t=8

there are integral tables to handle the 1/(t^2+1) part

a couple are integral du/u = lnlul + c

and another integral du/(u^2+a^2 = (1/a)arctan(u/a) + c

in the 2nd one, u would be t and a=1

integral of 5 is 5t, evaluated at 0 to 8 is 5(8)-4(0) = 40

that leaves finding the integral of 200/(t^2+1) dt

it's = 200 times the integral of dt/(t^2+1)

Answer 2

I hope the video helps, Keira. It is a complicated topic at first hearing but once you realize you are adding rectangles' areas, it is cumbersome but not impossible. Please do not hesitate to contact me if you need further help.