Functions Defined by Integrals

Question

Pumping stations deliver oil at the rate modeled by the function D, given by D(t) = 5t/(1+3t) with t measure in hours and D(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? Give 3 decimal places.

Answer 1

The problem here, of course, is to integrate 5t/(1 + 3t) and then to evaluate that integral between 0 and 4.

 

I believe the integral to be as follow:

 

(5/3){t*ln(1+3t) - (1/3)[(1+3t)*ln(1+3t) - (1+3t)]}

 

You can do the numerical evaluation, BUT FIRST: you must check that I have done the integration correctly by differentiating the expression I wrote.  

 

Please send me a message if you have trouble!

If I do not hear from you, I will figure that the integral checked out.