Page 45 - Math SL HB Sem 2

Example 19: Functions f and g is being defined as
f(x) = lx-2l,xeR

g(x):x(3-x),xeR

. Find exact vatue of f t ft*l + g(x) dx. I Ans: 6]
)

We can produce an algebraic expression to determine the exact area finclosed by a curve. We
shall also find that the definite integral plays a large part in determining the area enclosed by a
curve.
As a starting point we consider a single rectangular strip.
Consider the function y : f(x) as shown below.

v
Upper rectangle
{ rr.- st)
frr)
Lower rectangle

(L x ,({ ')<-
:
Divide the interval from x : a to x b into n equal parts:
a: X0, Xl , X2,...- X1:b
b a
This mean that each sEip is of width , and denoted it to be 6x.
n