Integration word problem

  • Thread starter Momentum09
  • Start date
  • #1
71
0

Homework Statement


In a West Texas school district the school
year began on August 1 and lasted until May
31. On August 1 a Soft Drink company in-
stalled soda machines in the school cafeteria.
It found that after t months the machines
generated income at a rate of
f(t) =
500t/ (5t^2 + 2)
dollars per month. Find the total income,
$Tsec, produced during the second semester
beginning on January 1.


Homework Equations



I know to find the income we first have to find the integral for the function t. I did this and got 50 ln [5x^2 +2].
I set u = 5t^2 +2, so du = 10t dt

The Attempt at a Solution



I used 6 as my upper limit and 1 as my lower limit but I can't get the right answer. Can someone please tell me what is the right limit of integration to use in this case?
Thank you so much for your help!
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
Your limits are a little off. Why did you use 6? The machine was functioning for 5 months from Aug 1 to Jan 1 the next year. And it's not supposed to be 0 either for the lower limits. That ignores the revenue for the first month.
 

Related Threads on Integration word problem

  • Last Post
Replies
8
Views
8K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
3
Views
5K
Replies
6
Views
4K
Replies
3
Views
4K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
17
Views
2K
  • Last Post
Replies
7
Views
2K
Top