xLeviathan Wrote:The integral of the interval (-1, 1) = 0, then you can try different Riemann Sums or (I think) add the area of the trapezoids? (1/x forms trapezoids when delta x = 1).
This is completely assumption since i haven't ever come across a question like this in my studies yet, but a rough solution you could do the integrals between -1..1 and 1..9, then add them, surely?
First bit is right, the -1..1 part is = 0
The actual integral of the remaining part is exactly
2*ln(3)
or
2.197224578
between the values of 1 and 9
the maths
You tried using the trapezium rule, well thats not worth doing, that unfortunately only evaluates the answer, which gives you an incorrect sum here.
Since you can evaluate the integrals definitively between the 2 values, int(1/x) = ln(x)
Between 1 and 9 this gives
ln(9)-ln(1) = ln(9/1) = ln(9) = ln(3^2)=2ln(3) by logarithm laws