Numerical Analysis/Romberg Quiz

Point added for a correct answer:
Points for an incorrect answer:
Ignore the questions' coefficients:

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

	-1.2345435
	0.4761463020
	0.2345632784
	0.567894567

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 $I=\int _{a}^{b}f(x)\,dx$ is

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

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

	0.1997146621
	0.1345234567
	0.2345234234
	1.0000000000

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

	2.6
	1.6
	4.6
	5.6