Quiz Chapter 07.03: Simpson’s 1/3 Rule

1. The highest order of polynomial integrand for which Simpson’s 1/3 rule of integration is exact is

2. The value of\, \displaystyle\int_{0.2}^{2.2} e^{x} dx by using two-segment Simpson’s 1/3^rd rule is most nearly

3. The value of\, \displaystyle\int_{0.2}^{2.2} e^{x} dx by using four-segment Simpson’s 1/3^rd rule is most nearly

4. The velocity of a body is given by

• • • \begin{matrix} v(t) = 2t,&1 \leq t \leq 5 \\ v(t) = 5t^{2} + 3,& 5 < t \leq 14 \\ \end{matrix}

where t is given in seconds, and v is given in m/s. Using two-segment Simpson’s 1/3^rd rule, the distance covered in meters by the body from t=2 to t=9 seconds most nearly is

5. The value of\, \displaystyle\int_{3}^{19} f(x)dx by using two-segment Simpson’s 1/3^rd rule is estimated as 702.039. The estimate of the same integral using four-segment Simpson’s 1/3^rd rule is most nearly

6. The following data of the velocity of a body is given as a function of time.

The best estimate of the distance in meters covered by the body from t=4 to t=15 using combined Simpson’s 1/3^rd rule and the Trapezoidal rule would be