TASK 3

The curve y = xn is shown in figure 2.

[a] Choose any non-integer value of n which is greater than 1 but less than 3, and use integration to find the area under the curve between x = 1 and x-5.

[b] Now work out your value of y when x is halfway between 1 and 5, i.e. x=3 and use this to find the area of the rectangle ABCD.

[c] Work out the values of y when x is halfway between 1 and 3, and halfway between 3 and 5, i.e. x = 2 and x = 4. Using figure 3 to help you, work out the area of the rectangle between (1,0) and (3,0), and the area of the rectangle between (3,0) and (5,0). Add your two areas. What do you notice?