Numerical Analysis I, Fall 2010 (http://www.math.nthu.edu.tw/˜ wangwc/)

Quiz 05

Dec 17, 2010.

1. (40 pts) Integrate ∫_{0}^{1} e^{x^{2}}dx using Trapezoidal Rule. Estimate n or h it takes to bound the error within 10^{−6}. Then report your numerical answer to 9 digits.

2. (30 pts) Find the degree of precision for Simpson’s Rule. Give details.

3. (30 pts) Derive the error formula of (non-composite) Midpoint Rule for ∫_{a}^{b} f(x)dx. That is, give explicit formula of ∫_{a}^{b} f(x)dx − (b − a)f(\frac{a+b}{2}), assuming f is sufficiently smooth.

Numerical Analysis I, Fall 2010 (http://www.math.nthu.edu.tw/˜ wangwc/)

Quiz 05

Dec 17, 2010.

1. (40 pts) Integrate ∫_{0}^{1} e^{x^{2}}dx using Trapezoidal Rule. Estimate n or h it takes to bound the error within 10^{−6}. Then report your numerical answer to 9 digits.

2. (30 pts) Find the degree of precision for Simpson’s Rule. Give details.

3. (30 pts) Derive the error formula of (non-composite) Midpoint Rule for ∫_{a}^{b} f(x)dx. That is, give explicit formula of ∫_{a}^{b} f(x)dx − (b − a)f(\frac{a+b}{2}), assuming f is sufficiently smooth.