M371 - Alexiades
                  Problem Set 8 ( Do by hand, with a calculator )

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Consider the integral: I = ∫₀¹ x(1−x²) dx
1. Find the exact value.
2. Apply Trapezoidal Rule with h=1/2 and h=1/4. Is the reduction in the error about what you would expect ? Explain.
3. Apply Romberg on the Trapezoidal values you found in 2. Is it more accurate than Trapezoidal ?
4. Apply Simpson Rule with h=1/2 and h=1/4. Is the reduction in the error about what you would expect ? Compare with Trapezoidal and Romberg.


Which rule did best ? Explain.