BCA S3 Numerical methods - module2-set1-Kerala university

1. Explain the geometrical interpretation of trapezoidal rule. (2mark B-3849 KU 2016)

2. Derive the two point Gauss quadrature rule. (2mark B-3849 KU 2016)

3. Evaluate  by means of trapezoidal rule with n=10 (4mark B-3849 KU 2016)

4. Compute the integral  using Gaussian two point formula.(4mark B-3849 KU 2016)

5. Compute Romberg estimate for  (15 mark B-3849 KU 2016)

6. Comment on numerical integration. (2mark B-3899 KU 2016, 2mark 8237 KU 2015 )

7. Explain Simpson's 1/3rd rule. (2mark B-3899 KU 2016,2mark 8237 KU 2015)

8. Evaluate  using :
 a.  Trapezoidal rule
 b.  Simpson's 3/8th rule taking h=0.2 for both cases. (15 mark B-3899 KU 2016. )

9. Use trapezoidal rule to evaluate the approximate values of the definite integrals  given that
x            0         0.2         0.4           0.6            0.8          1.0
f(x)        0       0.1987    0.3894     0.5646      0.7174     0.8415
                                                                                                    (15 mark 8237 KU 2015. )

10. Evaluate  using Trapezoidal rule take h=0.1 
                                                                                                           (4mark 8237 KU 2015)

11. _________ is a numerical integration technique. (1mark 8237 KU 2015)

12. Formulae for numerical integration is called ___________(1mark 8237 KU 2015)