4
 (x
2
 2) dx = 15
1
Formula
b
 f ( x)dx = f ( x ) (b a)
*
a
4
 f ( x)dx = f ( x ) (b a)
*
1
4
 (x
2
 2)dx = ( x* ) 2  (4  1)
1
15 = ( x* ) 2  2  3
15
= ( x* ) 2  2
3
5  2 = ( x* ) 2
7 = ( x* ) 2
( x* ) 2 = 7
x* =  7
y = x 2  2 x and y = 3
comparing both equation
x2  2 x  3
x2  2 x  3 = 0
factorization
x 2  3x  x  3 = 0
x( x  3)  1( x  3) = 0
( x  1)( x  3) = 0
x 1 = 0
x 3 = 0
x = -1
x=3
x =  1,3
know we get
3  x2  2 x
so, subtract small function from l arg e function and apply int egral
y = 3 - (x 2  2 x)
y = 3 - x2  2x
3

1
find the area
3  x 2  2 x  dx

x3
x2 
A  3 x   2 
3
2

3

33
32  
( 1)3
12 
A  3*3   2   3(1) 
2
3
2 
3
2 

1 

A  9  9  9 -  3   1
3 

1

A  9 -  2  
3

1
A  9 +2 3
1
A  11 3
33-1 32
A
=
ans :
3
3