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

Answer
Answer. a

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

Answer
Answer. b

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

Answer
Answer. d

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

Answer
Answer. d

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

Answer
Answer. c

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

Answer
Answer. a

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

Answer
Answer. d

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