From 08df82310f54ae4ef2d31f5cc5c37c09c93285fa Mon Sep 17 00:00:00 2001
From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Wed, 22 Aug 2018 21:19:44 +1000
Subject: [PATCH] antiderivatives, photoelectric energy

---
 physics/light-matter.md |  3 ++-
 spec/calculus.md        | 23 +++++++++++++++++++++++
 2 files changed, 25 insertions(+), 1 deletion(-)

diff --git a/physics/light-matter.md b/physics/light-matter.md
index a44f583..940605b 100644
--- a/physics/light-matter.md
+++ b/physics/light-matter.md
@@ -29,6 +29,7 @@ $$ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$$
 - $V_{\operatorname{supply}}$ does not affect photocurrent
 - if $V_{\operatorname{supply}} \gt 0$, e- are attracted to collector anode.
 - if $V_{\operatorname{supply}} \lt 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$
+- not all electrons have the same velocity - depends on ionisation energy (shell)
 
 #### Wave / particle (quantum) models
 wave model:  
@@ -55,7 +56,7 @@ particle model:
 
 $$\phi=hf_0$$
 
-#### $E_K$ of photoelectrons
+#### $E_K$ of photoelectrons (stopping energy)
 
 $$E_{\operatorname{k-max}}=hf - \phi$$
 
diff --git a/spec/calculus.md b/spec/calculus.md
index a5f3346..8476412 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -171,3 +171,26 @@ $${d(\log_e x)\over dx} = x^{-1} = {1 \over x}$$
 
 <!-- $${d(ax^{nx}) \over dx} = an \cdot e^nx$$ -->
 
+## Antidifferentiation
+
+$$y={x^{n+1} \over n+1} + c$$
+
+## Integration
+
+$$\int f(x) dx = F(x) + c$$
+
+- area enclosed by curves
+- $+c$ should be shown on each step without $\int$
+
+$$\int xn = {x^{n+1} \over n+1} + c$$
+
+### Integral laws
+
+$\int f(x) + g(x) dx = \int f(x) dx + \int g(x) dx$  
+$\int k f(x) dx = k \int f(x) dx$  
+
+| $f(x)$ | $\int f(x) \cdot dx$ |
+| ------ | -------------------- |
+| $k$ (constant) | $kc + c$ |
+| $x^n (n \in J\\\{-1\})$ | ${1 \over {n+1}}x^{n+1} + c$ |
+
-- 
2.47.1