Numerical Analysis/Romberg Quiz

{$$\int_0^3 \frac{sin(2x)}{1+x^2}\,dx $$ - -1.2345435 + 0.4761463020 - 0.2345632784 - 0.567894567
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{ Romberg Integration is an extrapolation formula of the trapezoidal rule for integration. +TRUE. -FALSE.
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{True error in a multiple segment Trapezoidal rule with n segments for an integral $$ I = \int_a^b f(x) \,dx $$ is + $$ E_t = \frac{(b-a)^3}{12n^2}\frac{\sum_{i=1}^nf''(\xi_i)}{n} $$ - $$ E_t = \frac{(b)^3}{11n^2}\frac{\sum_{i=1}^nf''(\xi_i)}{n} $$ - $$ E_t = \frac{(b-a)^3}{12n^2}$$ - $$ E_t = \frac{\sum_{i=1}^nf''(\xi_i)}{n}$$
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{$$\int_0^3 sin(4x)e^{-2{x}}\,dx$$ +0.1997146621 -0.1345234567 -0.2345234234 -1.0000000000
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{$$\int_{0.04}^1 \frac{1}{\sqrt{x}}\,dx $$ -2.6 +1.6 -4.6 -5.6
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