# Numerical Analysis/Romberg Quiz

1 ${\displaystyle \int _{0}^{3}{\frac {sin(2x)}{1+x^{2}}}\,dx}$

 -1.23454 0.476146 0.234563 0.567895

2 Romberg Integration is an extrapolation formula of the trapezoidal rule for integration.

 TRUE. FALSE.

3 True error in a multiple segment Trapezoidal rule with n segments for an integral ${\displaystyle I=\int _{a}^{b}f(x)\,dx}$ is

 ${\displaystyle E_{t}={\frac {(b-a)^{3}}{12n^{2}}}{\frac {\sum _{i=1}^{n}f''(\xi _{i})}{n}}}$ ${\displaystyle E_{t}={\frac {(b)^{3}}{11n^{2}}}{\frac {\sum _{i=1}^{n}f''(\xi _{i})}{n}}}$ ${\displaystyle E_{t}={\frac {(b-a)^{3}}{12n^{2}}}}$ ${\displaystyle E_{t}={\frac {\sum _{i=1}^{n}f''(\xi _{i})}{n}}}$

4 ${\displaystyle \int _{0}^{3}sin(4x)e^{-2{x}}\,dx}$

 0.199715 0.134523 0.234523 1

5 ${\displaystyle \int _{0.04}^{1}{\frac {1}{\sqrt {x}}}\,dx}$

 2.6 1.6 4.6 5.6