1. a. Complete the table below for the values of y = x3
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x
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2
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3
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4
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5
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6
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7
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8
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y
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b. Use Simpson's Rule with and the table of values to find the approximate area between the curve y = x3, the x-axis and the lines x = 2 and x = 8.
2. Use the Simpson's Rule, with six 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.
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x
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2
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3
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4
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5
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6
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7
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8
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9
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10
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y
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b. Use Simpson's Rule with eight intervals 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. Complete the table for values of y = sin(x2), where x is in radians. Give each value correct to 3 decimal places.
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x
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0
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0.25
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0.5
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0.75
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1
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y
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b. Use Simpson's Rule and the above table to estimate
.
5. Evaluate the following integrals using Simpson's Rule with the given trapezium widths:
a.
with h = 1
b.
with h = 0.5
