Answer:
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By the fundamental theorem of calculus,
Now the arc length over an arbitrary interval
is
But before we compute the integral, first we need to make sure the integrand exists over it.
is undefined if
, so we assume
and for convenience that
. Then
The two trapezoidal faces together have an area of
.. (5 in)*(5 in +9 in) = 70 in^2
The remaining surface can be unfolded to an area that is
.. (5 in)*(5 in +9 in +6.4 in +5 in) = 127 in^2
Together, these add to
.. 70 in^2 +127 in^2 = 197 in^2 . . . . . . . the 4th selection