Trapezium

Well, my A/S level Maths Exam is on monday, so i've decided to try a past paper. The first question is

1. Use the Trapezium Rule with five ordinates to find an approximate value for:

[intergration sign with limits 1 and 0] Sq root(1 + x^3) dx

Show your working and give your answer correct to two decimal places

This is something that my maths teacher skipped (due to lack of time) and i have no idea on how to di it. Could someone please tell me:

1. The Trapezium Rule
2. How to use the Trapexium Rule for intergration

Thanks in advance.

The trapezium rule is a method of numerical integration similar to euler's method or Simpson's rule.
Let's say that we have a function f(x) which is continous over x and we want to integrate it between the two points a and b. With the trapezium rule, we divide the interval [a b] into smaller parts (in your example 5) and calculate the area below the graph (which represents the integral in this one-dimensional case) with the following equation:
A = (f(x) + (f(x) + f(x+deltax))/2)*deltax
where deltax is the current small interval over x.
You can think of this area as a rectangle with a triangle on top, following the function's values in the points x, x+deltax. Calculate all these areas over all the small intervals and sum them up to get the total numerical approximation of the integral.

Thanks for the reply, however i've already found out and use the following formula:

A = h/2 (y0+yn+2(y1 + y2 + ... + y(n-1)))

and luckily, it was the first question of the exam and was really easy.
Thanks again

(if a mod wants to lock this, he can do)