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Trapezoidal Approximation Error

Thread starter theBEAST
Start date Sep 30, 2012
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Approximation Error

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1 reply · 2K views · last reply Oct 1, 2012

theBEAST

Thread starter
Sep 30, 2012

#1

Homework Statement

Text problem: approximate the integral of f(x) dx from 0 to 2 using the Trapezoid Rule, where K2 = max over x in [0,2] of |f''(x)| < a, with a = 3. Asks for the smallest number of subintervals N to guarantee accuracy to 2 decimal places.

The Attempt at a Solution

Handwritten derivation on lined paper of a trapezoidal error bound: |E_T| ≤ K(b-a)^3/(12n^2) ≤ 0.005, then 0.005 ≥ 3(2)^3/(12n^2), n^2 ≥ 3·2^3/(12(0.005)), n ≥ 20, n > 20.

Thus my answer is N = 20.

I wasn't sure if I should use ≤ or just <. Also to get 2 decimal place accuracy would using 0.005 be correct?

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Mark44

Mentor

Insights Author

Oct 1, 2012

#2

theBEAST said:

Homework Statement

The Attempt at a Solution

Thus my answer is N = 20.

I wasn't sure if I should use ≤ or just <. Also to get 2 decimal place accuracy would using 0.005 be correct?

Your work looks fine to me, but I think I would use < instead of ≤. If your error < .005, you'll be guaranteed 2 decimal place accuracy.

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