3^{y} is a sawtooth function, repeating every 1 unit change in y.
So Integral, 0 to 5, of 3^{y} dy is 5 * Integral, 0 to 1, of 3^y dy, as y={y} in that interval.
3^y = e^(y*ln(3))
so
Integral, 0 to 1, of 3^y dy = Integral, 0 to 1, of e^(y*ln(3)) dy = [(3^y) / ln3] evaluated from 0 to 1 = 3/ln3  1/ln3 = 2/ln3.
Five times that is 10/ln3 ~= 9.102392266268373

Posted by Charlie
on 20071012 11:06:04 