Recent questions tagged integration-by-trapezoidal-and-simpsons-rule / GO Mechanical

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GATE Mechanical 2021 Set 2 | Question: 18
Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is $1.83$ $1.60$ $1.51$ $1.06$

Value of $\int_{4}^{5.2} \ln x\: dx$ using Simpson’s one-third rule with interval size $0.3$ is$1.83$$1.60$$1.51$$1.06$

go_editor

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go_editor asked Mar 1, 2021

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GATE2020-ME-2: 35
For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end points, is ________ (round off to one decimal place).

For the integral $\displaystyle \int_0 ^{\pi/2} (8+4 \cos x) dx$, the absolute percentage error in numerical evaluation with the Trapezoidal rule, using only the end poin...

go_editor

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go_editor asked Sep 18, 2020

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GATE2020-ME-1: 26
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields $0.914$ $1.248$ $0.581$ $0.592$

The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields$0.914$$1.2...

go_editor

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go_editor asked Feb 19, 2020

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GATE2019 ME-1: 18
Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______

Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______

Arjun

28.5k points

Arjun asked Feb 9, 2019

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GATE2017 ME-1: 29
$P(0, 3), Q (0.5, 4)$ and $R(1, 5)$ are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule within limits $x=0$ and $x=1$ for the curve. The difference between the two results will be $0$ $0.25$ $0.5$ $1$

$P(0, 3), Q (0.5, 4)$ and $R(1, 5)$ are three points on the curve defined by $f(x)$. Numerical integration is carried out using both Trapezoidal rule and Simpson's rule w...

Arjun

28.5k points

Arjun asked Feb 26, 2017

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GATE2016-2-29
The error in numerically computing the integral $\int_{0}^{\pi }(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between $0$ and $\pi$ is ___________

The error in numerically computing the integral $\int_{0}^{\pi }(\sin x+\cos x)dx$ using the trapezoidal rule with three intervals of equal length between $0$ and $\pi$ i...

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-3-13
Using a unit step size, the value of integral $\int_{1}^{2}x \ln x dx$ by trapezoidal rule is ________

Using a unit step size, the value of integral $\int_{1}^{2}x \ln x dx$ by trapezoidal rule is ________

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE2015-2-29
The values of function $f(x)$ at $5$ discrete points are given below: $\begin{array}{|l|l|l|l|l|l|} \hline x & 0& 0.1 & 0.2 & 0.3 & 0.4 \\ \hline f(x) & 0 & 10 & 40& 90 & 160 \\ \hline \end{array}$ Using Trapezoidal rule with step size of $0.1$, the value of $\int_{0}^{0.4}f(x)dx$ is __________

The values of function $f(x)$ at $5$ discrete points are given below:$$\begin{array}{|l|l|l|l|l|l|} \hline x & 0& 0.1 & 0.2 & 0.3 & 0.4 \\ \hline f(x) & 0 & 10 & 40& 90 ...

Arjun

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Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 3 | Question: 5
The definite integral $\int_{1}^{3}\dfrac{1}{x}$ is evaluated using Trapezoidal rule with a step size of $1$. The correct answer is _______

The definite integral $\int_{1}^{3}\dfrac{1}{x}$ is evaluated using Trapezoidal rule with a step size of $1$. The correctanswer is _______

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE ME 2013 | Question: 3
Match the CORRECT pairs: ... $P-2; Q-1; R-3$ $P-3; Q-2; R-1$ $P-1; Q-2; R-3$ $P-3; Q-1; R-2$

Match the CORRECT pairs:$\begin{array}{llll} & \text{Numerical Integration Scheme} & & \text{Order of Fitting Polynomial} \\ P. & \text{Simpson's 3/8 Rule} & 1. & \text{F...

piyag476

1.4k points

piyag476 asked Feb 19, 2017