The Trapezium Rule

Which among the following is true?

• Trapezium rule will give an estimate or approximate area under a curve.

• Trapezium rule is used to get an exact area under a curve

Which among the following is true?

• The trapezium rule works by splitting the area under a curve into a number of trapeziums of unequal width.

• The trapezium rule works by splitting the area under a curve into a number of trapeziums of equal width.

In the trapezium rule, h =?

 $\int_a^bf\left(x\right)dx=\frac{1}{2}h\left[y_o+2\left\{y_1+y_2+..y_n-1\right\}+y_n\right]$  

•  $h=\frac{upper\ \lim it+lower\ \lim it}{no:\ of\ intervals}$  

•  $h=\frac{upper\ \lim it\ -\ lower\ \lim it}{no:of\ intervals}$  

•  $h=\frac{lower\ \lim it\ -\ upper\ \lim it}{2}$  

Which of the following is true when using the Trapezium Rule?

(Tick as many as appropriate)

• The upper limit is the highest value of x

• The number of ordinates is 1 less than the number of strips

• The number of strips is 1 less than the number of ordinates

• The height of each strip is the difference in the x-values.

• The height of each strip is the average of the x-values.

If there are five strips, then there must be four ordinates.

• False

• True

If there are nine ordinates, then there must be eight strips.

• True

• False

Which of the following is true in the Trapezium Rule formula?

• The height h represents the difference between the x-values

• The ordinates can be obtained by integrating the function

• The first two ordinates are doubled

• The area under the curve is exact