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[spec] fundamental theorem of calculus
author
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 6 May 2019 07:22:21 +0000
(17:22 +1000)
committer
Andrew Lorimer
<andrew@lorimer.id.au>
Mon, 6 May 2019 07:22:21 +0000
(17:22 +1000)
spec/calculus.md
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spec/calculus.md
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spec/calculus.md
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$$f(x) = {P(x) \over Q(x)} \quad \text{where } P, Q \text{ are polynomial functi
- when two graphs have the same ordinate, $y$-coordinate is double the ordinate
- when two graphs have opposite ordinates, $y$-coordinate is 0 i.e. ($x$-intercept)
- when one of the ordinates is 0, the resulting ordinate is equal to the other ordinate
- when two graphs have the same ordinate, $y$-coordinate is double the ordinate
- when two graphs have opposite ordinates, $y$-coordinate is 0 i.e. ($x$-intercept)
- when one of the ordinates is 0, the resulting ordinate is equal to the other ordinate
+
+## Fundamental theorem of calculus
+
+If $f$ is continuous on $[a, b]$, then
+
+$$\int^b_a f(x) \> dx = F(b) - F(a)$$
+
+where $F$ is any antiderivative of $f$