Problem : Find the length of the graph of f (x) = (1/2)(e ^{x} + e ^{-x}) from x = 0 to b .
Since f'(x) = (1/2)(e ^{x} - e ^{-x}) , the length of the graph is equal to
dx | = | e ^{x} + e ^{-x} dx | |
= | (e ^{x} - e ^{-x}|_{0} ^{b}) | ||
= |
Problem : Find the length of the graph of g(x) = 2x ^{3/2} 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
9 dx | = | u ^{1/2} du | |
= | |_{19} ^{46} | ||
= | (46^{3/2} -19^{3/2}) |