Statistics and Numerical Methods: Unit IV: Interpolation, numerical differentiation and numerical integration
Exercise 4.5 (b) [Double integrals using Tapezoidal and Simpson's 1/3rd rules]
Solved Example Problems
[Double integrals using Tapezoidal and Simpson's 1/3rd rules]
EXERCISE 4.5 (b)
[Double integrals using Tapezoidal and Simpson's 1/3rd rules]
1.
Evaluate, 
dx dy, taking h = k = 0.5 by both Trape- zoidal rule and
Simpson's rule.
[Ans. T.R. 0.0413, S.R. 0.0408]
2.
Evaluate, 
by Trapezoidal rule and Simpson's rule.
[Ans.
T.R: 0.0349, S.R: 0.0349]
3.
Evaluate, 
log (x+2y) dx dy, taking Δx = 0.15, Ay = 0.25.
[Ans, T.R 0.4292, S.R.: 0.4296]
4.
Evaluate, the integral 
[Ans. 0.4899]
5.
Evaluate, the inegral 
using the Trapezoidal rule with h = k
= 0.5 and h = k = 0.25
[Ans.
0.343304, 0.340668] [A.U M/J 2016 R13]
6.
The following table gives the values of f (x, y) = ey sinx, over the
interval 0 ≤ x ≤ 0.2, 0 ≤ y ≤ 0.2.
Evaluate
the integral of f (x, y), over the interval 0 ≤ x ≤ 0.2, 0 ≤ y ≤ 0.2
(a)
by the Trapezoidal rule with h = 0.2
(b)
by the Trapezoidal rule with h = 0.1
(c)
by Simpson's rule with h = 0.1
[Ans.
(a) 0.004414, (b) 0.004413, (c) 0.004413]
Statistics and Numerical Methods: Unit IV: Interpolation, numerical differentiation and numerical integration : Tag: : Solved Example Problems - Exercise 4.5 (b) [Double integrals using Tapezoidal and Simpson's 1/3rd rules]
Related Topics
Related Subjects
Statistics and Numerical Methods
MA3251 2nd Semester 2021 Regulation M2 Engineering Mathematics 2 | 2nd Semester Common to all Dept 2021 Regulation