P1^

6

Areas

(^) below
(^) the
(^) x
axis
EXAMPLE 6.12 Find the area between the curve and the x axis for the function y = x^2 + 3 x
between x = − 1 and x = 2.
SOLUTION
The first step is to draw a sketch of the function to see whether the curve
goes below the x axis (see figure 6.17).
This shows that the y values are positive for 0  x  2 and negative for − 1  x  0.
You therefore need to calculate the area in two parts.
AreaAx xxd
xx

=+

=+







=+(

∫ ()

––

• 
  
  
  
  • 
    
  
  
  
  

2

1

0

32

1

0

3

3

3

2

(^01332) ))

=+

=+







=+

∫

–.

()

7

6

8

3

2

0

2

32

0

2

3

3

3

2

6

AreaBx xxd

xx

(()

=

=+

=

–

.

0

26

3

7

6

26

3

59

6

Totalarea

squareunits.

y

2 x

–1

A

B

y = x^2 + 3x

Figure 6.17