Posted by UMich1344 on .
The approximation to a definite integral using n=10 is 2.346; the exact value is 4.0. If the approximation was found using each of the following rules, use the same rule to estimate the integral with n=30.
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,
If 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