# Evaluating a definite integral when a condition is given

1. Jun 2, 2013

### justwild

1. The problem statement, all variables and given/known data
Given that x$^{2}$f(x)+f($\frac{1}{x}$)=0, then evaluate $\int$$^{1.5}_{0.6}$f(x)dx

2. Relevant equations

3. The attempt at a solution

tried to replace f(x) using the provided equation...didn't help

2. Jun 3, 2013

### Office_Shredder

Staff Emeritus
Can you elaborate on how you tried replacing f(x)?

3. Jun 3, 2013

### haruspex

Have you looked at what happens if you substitute y = 1/x in the integral and the use the equation to substitute for f(1/y)?
(Are you sure you've quoted the bounds correctly? It's not from a lower bound of 0.66666... by any chance?)

4. Jun 5, 2013

### justwild

well If I do that I shall be returning to the same problem statement...

5. Jun 5, 2013

### Ray Vickson

If the lower limit in the integral is 0.6, you cannot answer the question without knowing more about the function f(x). If the lower limit is 0.6666.... = 2/3, you can answer the question without knowing more about f(x).

The substitution u = 1/x DOES work if you do it judiciously!