Economics - Find increase of cost

[suspenc3]

Im not sure if anyone can help me with this, I haven't seen a question like this I am guessing its easy. I tried just taking the integral and evaluating, bu tthat gave me a wrong answer.

Q:The marginal cost of producing x units of a certain product is 74+1.1x-0.002x^2+0.00004x^3. Find the increase in cost if the production level is raise from 1200 to 1600

 

[arildno]

Well, isn't marginal cost the derivative of the cost with respect to the number of goods produced??

In that case, you integrated incorrectly.

 

[suspenc3]

Yes that is what I thought, but the answer I got was slightly off the given answer

 

[0rthodontist]

Well, IF you integrated correctly, then maybe the problem meant for you to take "marginal cost" literally as the cost of producing one more unit. In this case you would have to take a sum rather than an integral. Or maybe they wanted you to approximate by considering the cost of the nth unit to be the integral from n-.5 to n+.5 of the marginal cost--in this case you would integrate from 1200.5 to 1600.5

 

[suspenc3]

Oops..Must have made a mistake..Integration from 1600 to 1200 yields the correct answer