Question

The curve of the equation y = x+ 2x2, has x = ½ and x = 0 as x-intercepts. The area bounded by the x-axis, x = ½ and x = 3 is shown by the sketch below.

Find

1. 
   
2. The exact area bounded by the curve, x axis x= -½ and x=3 (Give your answer to 2dp)

Answer 1

1. 
   
   x²/2 + 2/3x3 + c
    
2. The exact area bounded by the curve, x axis 
   x= -½ and x=3 (Give your answer to 2dp)
   
   =0-(1/8 – 1/12)
   = - (3-2)
          24
   = - 1/24 ∴ 1/24
   32/2 + 2/3 x 33 __(0)
   9/2 + 54/3
   4.5 + 18 = 22.5
   Total area = 1/24 + 22.5=0.0416 + 22.5
   = 22.54