Question

I don't understand how to use the trapezium rule.
Example question attatched

Answer 1

The trapezium rule is a way of estimating the area under a curve. We know that the area under a curve is given by integration, so the trapezium rule gives a method of estimating integrals. This is useful when we come across integrals that we don't know how to evaluate.

The trapezium rule works by splitting the area under a curve into a number of trapeziums, which we know the area of.
If we want to find the area under a curve between the points x0 and xn, we divide this interval up into smaller intervals, each of which has length h (see diagram above).

Then we find that:



where y0 = f(x0) and y1 = f(x1) etc

Answer 2

Right, but I don't know how to apply the general equation for this question

Answer 3

Give a sec I didnt check the question...

Answer 4

http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch8.pdf pretty chill examples explain it better than anyone could.

Answer 5

well there are several ways to do the problem, the basic rule is

Area apprx = height/2 ( 1st + last + 2 times the middle values)

so in your table of values h = 0.5 1st y = 1.2 last y = 2 and the its 2* the sum of the middle values

\[A \approx \frac{0.5}{2}[ 1.2 + 2 + 2\times (4 + 5.7 + 5.5 + 4.2 + 3.6)]\]

Answer 6

height is the difference in the x values,

1st, last and middle are the y values of f(x) values.. for specific x's