anonymous
  • anonymous
On the Session 50 Worked Example a (MVT, FTC1 stuff), how did the lower bound equal 1.2? Thanks!
OCW Scholar - Single Variable Calculus
katieb
  • katieb
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anonymous
  • anonymous
Doesn't matter what the lower bound is as long as the antiderivative (F) is defined at that point. Because the lower point is fixed it yields a constant to the antiderivative and thus after differentiation it's gone. Example: \[\frac{ d }{ dx }\int\limits_{1}^{x}\frac{ 1 }{ t } dt = \frac{ d }{ dx } (\ln \left| x \right| - \ln \left( 1 \right)) = \frac{ 1 }{ x }\] You could substitute any positive constant value in place of 1 and the result would have been just the same.

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