Sometimes Simpsons Rule Performs Poorly Calculate M10 and S10 for the integral 1 0 1 x2
Chapter 7, Problem 64(choose chapter or problem)
Sometimes Simpsons Rule Performs Poorly Calculate M10 and S10 for the integral 1 0 1 x2 dx, whose value we know to be 4 (one-quarter of the area of the unit circle). (a) We usually expect SN to be more accurate than MN . Which of M10 and S10 is more accurate in this case? (b) How do you explain the result of part (a)? Hint: The error bounds are not valid because |f (x)| and |f (4)(x)| tend to as x 1, but |f (4)(x)| goes to infinity more quickly.
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