[spec] fundamental theorem of calculus

diff --git a/spec/calculus.md b/spec/calculus.md
index 01218996b723a7650e38ea770fb8150b31481855..b4540728a25ac9152219336c09153889850573d9 100644 (file)
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -290,7 +290,11 @@ Use identities:
 
 - $\sin^2x={1 \over 2}(1-\cos 2x)$
 - $\cos^2x={1 \over 2}(1+\cos 2x)$
-- $\sin 2x = 2 \sin x \cos x
+- $\sin 2x = 2 \sin x \cos x$
+
+### Partial fractions
+
+On CAS: Action $\rightarrow$ Transformation $\rightarrow$ `expand/combine`
 
 
 ## Applications of antidifferentiation
@@ -322,3 +326,11 @@ $$f(x) = {P(x) \over Q(x)} \quad \text{where } P, Q \text{ are polynomial functi
 - when two graphs have the same ordinate, $y$-coordinate is double the ordinate
 - when two graphs have opposite ordinates, $y$-coordinate is 0 i.e. ($x$-intercept)
 - when one of the ordinates is 0, the resulting ordinate is equal to the other ordinate
+
+## Fundamental theorem of calculus
+
+If $f$ is continuous on $[a, b]$, then
+
+$$\int^b_a f(x) \> dx = F(b) - F(a)$$
+
+where $F$ is any antiderivative of $f$