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January 29, 2015

January 29, 2015

Posted by **UMich1344** on Monday, September 29, 2008 at 10:05pm.

A) Left Rule

B) Trapezoid Rule

The section deals with approximation errors of definite integrals.

The error in the first approximation is 1.654. I'm not sure if that is relevant in this problem, but I imagine it would be since that's the topic of the section.

- Calculus - Derivatives -
**Scott**, Monday, February 24, 2014 at 6:15pmIf the original estimate was done by LEFT then the error is inversely proportional to the number of steps and the n = 30 error is (10/30) * -1.654 = -.551, approximately. So the estimate for n = 30 would be -.551 + 4.000 = 3.449

If the original estimate was done by TRAP then the error is inversely proportional to the square of the number of steps and the n = 30 error is (10/30)^2 * -1.654 = -.184, approximately. So the estimate for n = 30 would be -.184 + 4.000 = 3.816

If the original estimate was done by SIMP then the error is inversely proportional to the fourth power of the number of steps and the n = 30 error is (10/30)^4 * -1.654 = -.020, approximately. So the estimate for n = 30 would be -.02 + 4.000 = 3.980

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