Here's a problem. Not sure if I should just sub in or firstly integrate and then sub in. Please help..
an oil company found that the rate of oil production from an oil well is given by a function of time t, in years:
R(t) = [ 60t/t^2 +9 ] + 35
Approx. how many barrels of oil will be produced in the first 5 years of production?!
Thank you very much for that tip!!!
But another question is . What happens to the constant (35) when integrating. DO i just ignore it?!
So, (im not sure how to use the integration sign on the computer)
'Integration sign (0-5 years) = |' [60t/t^2+9] +53 dt
= 60/2 | [1/t^2+9] 2t dt
let u = t^2 +9
then du = 2t dt (?)
= 60/2 | 1/u du
= 60/2 ln |u| + c
= 30 ln (t^2 +9 )
= 30 ln 34 - 30 ln 9
= 105.8 - 65.92
= approx. 40 ?
I really appreciate your help !!