5.3 The Fundamental Theorem of Calculus: Difference between revisions

Revision as of 20:03, 23 August 2022

1. FTC #1

{\frac {d}{dx}}\int _{a(x)}^{b(x)}f(t)dt=b'(x)f(b(x))-a'(x)f(a(x))

2. FTC #2

\int _{a}^{b}f(x)dx=F(b)-F(a)

Where

{\frac {d}{dx}}\left[F(x)\right]=f(x)

.

F(x)

is called the antiderivative of

f(x)

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 [[5.3 The Fundamental Theorem of Calculus/33|33]]
 [[5.3 The Fundamental Theorem of Calculus/35|35]]
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-[[5.3 The Fundamental Theorem of Calculus/33|39]]
+[[5.3 The Fundamental Theorem of Calculus/39|39]]
-[[5.3 The Fundamental Theorem of Calculus/35|41]]
+[[5.3 The Fundamental Theorem of Calculus/41|41]]