It can't be done . . .
Suppose we have the function: .
We have its graph:Code:| / | oQ | /: | 2/ : | / : | oP : | /: : | / : : |/ : : ------+---+---+-- /| a b / | |
And you are looking for the interval where ?
am thinking about the idea if i know the arc length of spific function
then am asked to know the upper and lower limit
if the lower limit is given and am asked to find the upper limit
it will be easy, as an exaple suppose the arc lenght of f = 5
on [1,Z] find the number z ?
it will be easy I will integrated it as an definite integral then it will be something in terms of z = 5
and solve it
But am asking if the lower and upper limit are unknows, it is possible to find them ? WITHOUT any another given in the problem ?
maybe if the interval is [-Z,Z] and if the function is odd/even
it will be easy a little bit
but if the inteval is [a,b] , not from -a to a