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I am reading this text and I don't get the proof:

enter image description here

I don't see how the FTC2 is applied a second time. Where did the second set of equations come from?

Where did the $u$ come from? And by "second time" do they mean "let's apply FTC2 to a completely different equation and show we get the same result?"

Jwan622
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You look at $F(g(b))-F(g(a))$ in two different ways.

  • $F(g(b))-F(g(a))=F(g(x))|_{a}^{b}$
  • $F(g(b))-F(g(a))=F(u)|_{g(a)}^{g(b)}$
cansomeonehelpmeout
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  • I see, so "lets apply FTC2 a second time" doesn't mean applying FTC to the result of the first equation right? But just to a completely different equation? – Jwan622 Apr 11 '18 at 18:46
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    Yes, you're right. They're not using FTC twice in a row on the same expression, they are using it on another function. – cansomeonehelpmeout Apr 11 '18 at 18:48