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|
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