AdvancedNumeric answer

Integrating an exponential · Part 3 of 3

You integrate $f(x) = e^x$ over $[0, 1]$ numerically. The exact value is $e - 1 \approx 1.718282$ , so every estimate can be checked.

The trapezoid error with $n$ equal intervals is close to $\frac{h^2}{12}\left(f'(1) - f'(0)\right)$ , where $h = 1/n$ . What is the smallest $n$ that brings the error below $10^{-6}$ ?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

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Numerical integration: trapezoid, Simpson and Gauss

The trapezoid error with nnn equal intervals is close to h212(f′(1)−f′(0))\frac{h^2}{12}\left(f'(1) - f'(0)\right)12h2​(f′(1)−f′(0)), where h=1/nh = 1/nh=1/n. What is the smallest nnn that brings the error below 10−610^{-6}10−6?

More numerical methods questions

The trapezoid error with $n$ equal intervals is close to $\frac{h^2}{12}\left(f'(1) - f'(0)\right)$ , where $h = 1/n$ . What is the smallest $n$ that brings the error below $10^{-6}$ ?