Hi,

A little help required and some checking.

The trapezium rule, with 2 intervals of equal width , is to be used to find an approximate value for .

Explain, with the aid of a sketch, why the approximate value will be greater than the exact value of the integral.

My graphs are different from Wolfram's. Here they are: e^-x and -e^-x

EXPLANATION PART: I don't know this part. Help required.

Calculate the approximate and exact values respectively, to 3 d.p.

Another approximation to , is to be calculated by using two trapezia of unequal width. The first trapezium has width and the second has width , so that the three ordinates are at , and . Show that the total area of these two trapezia is given by .

Width and

, ,

Show that the value of for which is a minimum is given by .