Problem Involving Maximizing the Ratio of Integrals

  • Thread starter hartran
  • Start date
The ratio of integrals

∫〖a(x) b(x)dx〗/ ∫c(x) b(x)dx

can be maximized by choosing b(x) equal to the delta function at the point where a(x)/c(x) is a maximum.

Can anyone provide the solution for choosing b(x) when b(x) cannot equal the delta function, b(x) is greater than zero with a maximum value of C, and a(x) and c(x) are both positive over the integration interval and also monotonically increasing?
 

mathman

Science Advisor
7,632
378
I suspect the best you could do is take an interval around the x where a(x)/c(x) is maximum. The width of the interval would be 1/C, while b(x) = C in the interval, and = 0 otherwise.
 

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Hot Threads

Top