If 9 is continuous on (I), prove that fe gk ds ~ fe 9 ds as k
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If 9 is continuous on ¢(I), prove that fe gk ds ~ fe 9 ds as k ~ 00.
S. Let (¢,1) be a parametrization of a smooth arc in Rm, and let T : J ~ R be a C1 function, 1-1 from J onto I. If T'(U) =f ° for all but finitely many u E J,
'!/J = ¢ 0 T, and 9 : ¢(I) ~ R is continuous, prove that 1 g(¢(t))II¢'(t)11 dt = 1 g('!/J(u)) II '!/J' (u) II duo
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