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Problems 4
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
  9 dx | = |  u1/2du | |
| = |   |1946 | ||
| = |  (463/2 -193/2) |
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