1. Simpson’s 1/3 rule is used to integrate the function $f(x)=\frac{3}{5}x^2+\frac{9}{5}$ 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
\[\int_{0}^{0.8}(0.2+25x-200x^2+675x^3-900x^4+400x^5)dx\]
- 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
\[\int_{0}^{4}(x^4+10)dx\]
- 0.36
- 0.48
- 0.20
- 0.53
4. The estimate of $\int_{0.5}^{1.5}(\frac{1}{x})dx$ 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 $\int_{1}^{3}(\frac{1}{x})dx$, 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
