Page 41 - Math SL HB Sem 2

RECAP: $61x1+c;= rlxy
ox
Integrate both sides w.r.t. x + I fer.l*"lux = Jrlxpx

F(x)+c: I(x)dx

in more familiar form r{*) *.
Jr{')a*:

FAMILIES OF CURVES

Let's consider the following:

rJ2 _r' *"
.r:f xdx
If we want to draw the graph of y we find that there are more than one curve, i.e. a family of
,
curves, each of which has a different value for c
c=4

c:0

c= -2

c:-8

BASIC RULES OF INTEGRJITION

1. Jldx = x+c

2. Ikdx =kx + c, where k is aconstant

- .. n+l
3. xndx='-ag
J
n+l
J
+. t f1x; dx:ki f(x) dx where k is a constant
:
s. r1x; + g(x) dx l (x) dx + g(xy ax
J 1 I J