1. Simpson’s 1/3 rule is used to integrate the function between x = 0 and x = 1 using the least number of equal sub-intervals. The value of the integral is

- 22
- 44
- 55
- 33

2. For step-size, Δx = 0.4, the value of the following integral using Simpson’s 1/3 rule is

- 1.258
- 1.367
- 1.000
- 1.874

3. The magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s 1/3 rule. Take the step length as 1

- 0.36
- 0.48
- 0.20
- 0.53

4. The estimate of obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by

- 0.235
- 0.068
- 0.024
- 0.012

5. The integral , when evaluated by using Simpson’s 1/3 rule on two equal subintervals each of length 1, equals

- 1.000
- 1.098
- 1.111
- 1.120

6. The table below gives values of a function F(x) obtained for values of x at intervals of 0.25.

x |
0 | 0.25 | 0.5 | 0.75 | 1 |

F(x) |
1 | 0.9412 | 0.8 | 0.64 | 0.50 |

The value of the integral of the function between the limits 0 and 1 using Simpson’s rule is

- 0.7854
- 2.3562
- 3.1416
- 7.5000

7. Match the correct pairs

Numerical Integration Scheme |
Order of Fitting Polynomial |

P. Simpson’s 3/8 rule | 1. First |

Q. Trapezoidal rule | 2. Second |

R. Simpson’s 1/3 rule | 3. Third |

- P-2, Q-1, R-3
- P-3, Q-2, R-1
- P-1, Q-2, R-3
- P-3, Q-1, R-2