## laylam25 3 years ago Anyone know how to do this problem? The marginal cost of producing the xth box of light bulbs is 3 + x^2/1,000 dollars. Determine how much is added to the total cost by a change in production from x = 40 to x = 100 boxes.

1. p505

How is marginal cost related to total cost?

2. Chlorophyll

@laylam25 Look back how I solved your recent post!

3. mark_o.

i didnt see whatchloropyl have done do you have the link? any way is this correct 3 + (x^2/1,000) or maybe this is (3 + x^2)/1,000

4. mark_o.

@ laylam25

5. laylam25

oh this is similar to that?!

6. laylam25

its actually just written just like this: 3 + x^2/1,000

7. laylam25

This is actually under the chapter of the "definite integral: fundamental theorem of calculus" so I am guessing I have to incorporate that somewhere :/

8. Chlorophyll

Total Cost is Integral of Marginal Cost! => Integrate from 40 to 100

9. Chlorophyll

The difference between 40 and 100 boxes is the added cost!

10. mark_o.

total cost = integral of marginal cost marginal cost = integral (3 + x^2/1,000) ? can you start this ? what did you get?

11. mark_o.

that is integral from 40 to 100

12. mark_o.

$\int\limits_{49}^{100}(3+\frac{ x ^{2} }{ 1000 })dx=?$

13. mark_o.

i assumed thats the correct function

14. mark_o.

is it [3x+ x^3/3(1000)] from 40 to 100 =?

15. mark_o.

is it [300 + (100)^3/3000]-[12+ (40)^3/3000] =?