Simpson Rule MCQ

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

1. 22
2. 44
3. 55
4. 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. 1.258
2. 1.367
3. 1.000
4. 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

\[\int_{0}^{4}(x^4+10)dx\]

1. 0.36
2. 0.48
3. 0.20
4. 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

1. 0.235
2. 0.068
3. 0.024
4. 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. 1.000
2. 1.098
3. 1.111
4. 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

1. 0.7854
2. 2.3562
3. 3.1416
4. 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

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