The model for the ability of a child to memorise measured on a scale from  to  is , on .

Where  is the childs age in years.

(a)

Find the average value of this model between the child s first and second birth days.

Average value of the function  on  is defined as .

In this case  and .

The average value of this model between the child s first and second birth days is

.

.

Consider .

Solve the integral using integration by parts.

Formula for integration by parts:.

Here  and .

Consider .

Apply derivative on each side with respect to .

.

Consider .

Apply integral on each side.

.

Substitute corresponding values in .

.

Substitute  in .

The average value of this model between the child s first and second birth days is .

(b)

Find the average value of this model between the child s third and fourth birth days.

The average value of this model between the child s first and second birth days is

.

.

Substitute .

The average value of this model between the child s first and second birth days is .

(a) The average value of this model between the child s first and second birth days is .

(b) The average value of this model between the child s first and second birth days is .