Problem : Find the length of the graph of f (x) = (1/2)(ex + e-x) from x = 0 to b.Since f'(x) = (1/2)(ex - e-x), the length of the graph is equal to
|dx||=||ex + e-xdx|
|=||(ex - e-x|0b)|
Problem : Find the length of the graph of g(x) = 2x3/2 from x = 2 and x = 5.Since g'(x) = 3, the length is given by dx. Making the change of variables u = 1 + 9x, we have
or approximately 16.98.