Integration

1

2

3

4

• Integration
• is needed to find the area under a curve

5
R
To find the area of region R, two definite
integrals have to be calculated
6

• The Trapezium Rule always gives an approximation
  less than the true value

7

• The area between the curve f(x), the
• x-axis, x 1 and x 4 is given by

8

• The area below the x-axis is always negative

9

• The Trapezium Rule using 10 strips will give a
  more accurate approximation than one using 5
  strips

10

• Cavalieri was the first to think of an area as
  being made up of the sum of an infinite number of
  components
• He showed, using these methods, that the integral
  of xn from 0 to a was an1/(n 1)