In this question, you are asked to find estimates of the definite integral
⌠
⌡ 4
0 cos( x1/2 ) dx
by the Trapezoidal Rule and Simpson's Rule, each with 4 subintervals.
8.1 (1 mark)
Firstly, in the top row below enter x0, x1, ..., x4,
and in the cell below each xi, enter the value of f(xi).
To what accuracy, you ask? Well, that should really depend on the error bound of the Rule, but let's say 6 decimal place accuracy, and the final answer will be accepted, if it's correct to 4 decimal places.
xi in top row, f(xi) in bottom row: You have not attempted this yet
8.2 (1 mark)
Now, give the Trapezoidal Rule estimate T4 for the value of the integral correct to 4 decimal places.
T4 ≈
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8.3 (1 mark)
Given that the maximum value of |f"(x)| on the interval [0, 4] is approximately 0.08333333333, what is a bound on the error ET of your answer above, to 6 decimal places.
|ET| ≤
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8.4 (1 mark)
Now, give the Simpson's Rule estimate S4 for the value of the integral correct to 4 decimal places.
S4 ≈
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8.5 (1 mark)
Given that the maximum value of |f(iv)(x)| on the interval [0, 4] is approximately 0.0005952380952, what is a bound on the error ES of your answer above, to 6 decimal places.
|ES| ≤