Write an algorithm to compute integration using Simpson's 1/3 rule. Evaluate integration of \[ \quad \quad \quad \quad ∫^30(3x2+2x−5)dx \] using Simpson's 1/3 rule.
Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (5Hrs.)
Chapter Study
BCA Semester 4 – Numerical Methods – Unit 3: Numerical Differentiation and Integration (5Hrs.)
Comprehensive questions and detailed answers for Unit 3: Numerical Differentiation and Integration (5Hrs.). Perfect for exam preparation and concept clarity.
7
Questions
35
Marks
Write an algorithm to compute integration using Simpson's 1/3 rule. Evaluate integration of
using Simpson's 1/3 rule.
MediumTHEORY5 marks2021(TU FOHSS Final)
Using the trapezium rule, evaluate the integral
with 2 and 4 sub intervals. Compare with the exact solution. Comment on the magnitudes of the errors obtained.
MediumTHEORY5 marks2022(TU FOHSS Final)
For solving a linear system, compare Gauss elimination method and Gauss Jordan method. Why Gauss Seidel method is better than Jacobi's iterative method?
MediumTHEORY5 marks2022(TU FOHSS Final)
Using Euler's method find from
with h = 0.
MediumTHEORY5 marks2022(TU FOHSS Final)
Write an algorithm and program to calculate integration using Trapezoidal rule.
MediumTHEORY5 marks2023(TU FOHSS Final)
Use the Romberg method to get an improved estimate of the integral from x = 1.8 to x = 3.4 from the data in the table with h = 0.4.
| X: 1.6 | 1.8 | 2.0 | 2.2 | 2.4 | 2.6 | 2.8 | 3.0 | 3.2 | 3.4 | 3.6 | 3.8 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Y: 4.95 | 6.05 | 7.38 | 9.02 | 11.02 | 13.46 | 16.44 | 0.05 | 24.53 | 29.96 | 36.59 | 44.70 |
| : | 39 | 5 | 3 | 4 | 5 | 6 | 3 | 4 | 8 | 1 |
MediumTHEORY5 marks2024(TU FOHSS Final)
Write a program to compute integral Simpson's rule.
MediumTHEORY5 marks2024(TU FOHSS Final)
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Sample Questions
Using the trapezium rule, evaluate the integral \[ I=∫^01\frac{dx}{x2+6x+10} \] with 2 and 4 sub intervals. Compare with the exact solution. Comment on the magnitudes of the errors obtained.
Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (5Hrs.)
For solving a linear system, compare Gauss elimination method and Gauss Jordan method. Why Gauss Seidel method is better than Jacobi's iterative method?
Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (5Hrs.)
Using Euler's method find \(y(0.2)\) from \[ \frac{dy}{dx}=x+y,\quad y(0)=1\] with h = 0.
Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (5Hrs.)
Write an algorithm and program to calculate integration using Trapezoidal rule.
Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (5Hrs.)
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