Chapter Study

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 $x = 4.$

Time(x)	1	2	4	8	10
Distance(y)	0	1	5	21	27

MediumNumerical5 marks2081(TU Final)

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

∫^2_1\frac{e^x}{x}dx

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

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).

\int_{2}^{4} (x^3 + 2)\,dx

MediumNumerical5 marks2080(TU Final)

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 & 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

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

MediumNumerical5 marks2077(TU Final)

Evaluate the following integration using Romberg integration.

\int_{0}^{1} \frac{\sin^2 x}{x} \, dx

MediumNumerical5 marks2078(TU Final)

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