1. a. Complete the table below for the values of y = x2
x
|
2
|
3
|
4
|
5
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6
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7
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8
|
y
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b. Use the Trapezium Rule with six trapeziums and the table of values to find the approximate area between the curve y = x2, the x-axis and the lines x = 2 and x = 8.
2. Use the Trapezium Rule, with three intervals to find the shaded area shown below.
3. a. Complete the table below for the values of y = 1 / x.
Give values correct to 3 decimal places.
x
|
2
|
3
|
4
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5
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6
|
7
|
8
|
9
|
10
|
y
|
b. Use the Trapezium Rule with eight trapeziums and the table of values to find the approximate area between the curve y = 1 / x, the x-axis and the lines x = 2 and x = 10.
4. (Bursary Question)
Complete the table for values of y = sin(x2), where x is in radians. Give each value correct to 3 decimal places.
x
|
0
|
0.25
|
0.5
|
0.75
|
1
|
y
|
b. Use the Trapezium Rule and the above table to estimate .
5. Evaluate the following integrals using the Trapezium Rule with the given trapezium widths:
a. with h = 1
b. with h = 0.5