# Simpson Rule MCQ

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

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

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

1. 0.36
2. 0.48
3. 0.20
4. 0.53

4. The estimate of 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 , 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 0.5

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

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