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Bsc CSIT Semester 3 – Numerical Method – Unit 3: Numerical Differentiation and Integration (8 Hrs.)

Comprehensive questions and detailed answers for Unit 3: Numerical Differentiation and Integration (8 Hrs.). Perfect for exam preparation and concept clarity.

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What is numerical differentiation? The table below gives the values of distance travelled by a vehicle at various time interval, estimate the velocity and acceleration at x=4.x = 4.

Time(x)124810
Distance(y)0152127
MediumNumerical5 marks2081(TU Final)

What is an application of numerical integration? Find the value of the integral

∫12exxdx∫^2_1\frac{e^x}{x}dx

using Simpson’s 38\frac{3}{8}rule with n=6.n = 6.

MediumNumerical5 marks2081(TU Final)

How can we calculate derivatives of discrete (tabulated) functions? Write down its algorithm.

MediumNumerical5 marks2080(TU Final)

Find the following integral using composite trapezoidal rule for using 2 segments (k=2) and 4 segments (k=4).

∫24(x3+2) dx\int_{2}^{4} (x^3 + 2)\,dx
MediumNumerical5 marks2080(TU Final)

Estimate the integral value of following function from x=1.2x = 1.2 to x=2.4x = 2.4using Simpson’s 13\frac{1}{3} rule.

x1.01.21.41.61.82.02.22.42.6f(x)1.532.253.184.325.677.238.9810.9413.08\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 & 2.2 & 2.4 & 2.6 \\ \hline f(x) & 1.53 & 2.25 & 3.18 & 4.32 & 5.67 & 7.23 & 8.98 & 10.94 & 13.08 \\ \hline \end{array}
MediumNumerical5 marks2079(TU Final)

What is Gaussian integration formula? Evaluate the following integration using Gaussian integration three ordinate formula

∫01Sinxxdx\int_0^1 \frac{Sinx}{x} dx
MediumNumerical5 marks2079(TU Final)

Write down algorithm and program for the differentiating continuous function using three point formula.

MediumNumerical5 marks2077(TU Final)

How Simpson’s 13\frac{1}{3} rule differs from Trapezoidal rule? Drive the formula for Simson’s 13\frac{1}{3} rule.

MediumNumerical5 marks2077(TU Final)

Evaluate the following integration using Romberg integration.

∫01sin⁡2xx dx\int_{0}^{1} \frac{\sin^2 x}{x} \, dx
MediumNumerical5 marks2078(TU Final)
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Sample Questions

What is numerical differentiation? The table below gives the values of distance travelled by a vehicle at various time interval, estimate the velocity and acceleration at \(x = 4.\) |Time(x) |1 |2 |4

Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (8 Hrs.)

What is an application of numerical integration? Find the value of the integral \[∫^21\frac{e^x}{x}dx\] using Simpson’s \(\frac{3}{8}\)rule with \(n = 6.\)

Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (8 Hrs.)

How can we calculate derivatives of discrete (tabulated) functions? Write down its algorithm.

Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (8 Hrs.)

Find the following integral using composite trapezoidal rule for using 2 segments (k=2) and 4 segments (k=4). \[ \int{2}^{4} (x^3 + 2)\,dx \]

Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (8 Hrs.)

Estimate the integral value of following function from $x = 1.2$ to $x = 2.4$using Simpson’s $\frac{1}{3}$ rule. \[ \begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & 1.0 & 1.2 & 1.4 & 1.6 & 1.8 & 2.0 &

Marks: 5Chapter: Unit 3: Numerical Differentiation and Integration (8 Hrs.)

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Unit 3: Numerical Differentiation and Integration (8 Hrs.) chapter questions with answers for Numerical Method (Bsc CSIT Semester 3). Prepare for TU exams with our comprehensive question bank and model answers.