Page 39 - Math SL HB Sem 2

INTEGRATION

INDEFINITE INTEGRALS

Defurition : Anti derivative of a Function
A firnction F(x) is called an anti derivative of a function f(x) if and only if the
derivative ofF(x) is f(x).
i.e. l.t*l = r(*l I or F,(x): t(x) l
dx"
for all x in the domain of f(x).

d x'.
IOr exarnple: -. ( x
2'
ox -)
d .x'
(- +3) x
'2
=
dx
d
,*-',=*
dx
.d (F(x)+c)=f(x)
dx

A function x, f (x) has more than one anti derivatives F(x) + q.
,
,
The process of finding (F(x) + c) from f(x) or finding anti derivative of f(x): INTEGRATION
Jf(x)dx=F(x)+c

Example I : Show that F(x) is the anti derivative of f(x) if
a) F(x):( x+4)3 +c and f(x) = 3x2 +24x+48