Quiz Chapter 07.04: Romberg Method


(All Tests)


(More on Romberg Method)


(More on Integration)

Pick the most appropriate answer

1. If I_{n} is the value of integral\, \displaystyle\int_{a}^{b} f(x)dx using n-segment Trapezoidal rule, a better of the integral can be found using Richardson’s extrapolation as


2. The estimate of an integral of\, \displaystyle\int_{3}^{19} f(x)dx is given as 1860.9 using 1-segment Trapezoidal rule. Given f(7)=20.27, \, f(11)=45.125, and f(14)=82.23, the value of the integral using 2-segment Trapezoidal rule would most nearly be


3. The value of an integral\, \displaystyle\int_{a}^{b} f(x)dx given using 1-, \, 2-, and 4-segment Trapezoidal Rule is given as 5.3460, \, 2.7708, and 1.7536, respectively. The best estimate of the integral you can find using Romberg Integration is most nearly


4. Without using the formula for one-segment Trapezoidal Rule for estimating\, \displaystyle\int_{a}^{b} f(x)dx the true error, E_{t}, can be found directly as well as exactly by using the formula

      • E_{t} = -\dfrac{ \left( b - a \right)^{3}}{12} {f}''(\xi), \, a \leq \xi \leq b

5. For\, \displaystyle\int_{a}^{b} f(x)dx, the true error, E_{t}, in 1-segment Trapezoidal Rule is given by

      • E_{t} = - \dfrac{ \left( b - a \right)^{3}}{12} {f}'' ( \xi ), \, a \leq \xi \leq b

The value of \xi for the integral\, \displaystyle\int_{2.5}^{7.2} 3e^{0.2x}dx is most nearly


6. Given the velocity vs time data for a body

t(s) 2 4 6 8 10 25
v (m/s) 0.166 0.55115 1.8299 6.0755 20.172 8137.5

The best estimate for distance covered between 2s and 10s by using the Romberg Rule based on the Trapezoidal Rule’s results would be