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Recent questions tagged integration-by-trapezoidal-and-simpsons-rule
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GATE Civil 2021 Set 2 | Question: 46
Numerically integrate, $f(x)=10x-20x^2$ from lower limit $a=0$ to upper limit $b=0.5$. Use Trapezoidal rule with five equal subdivisions. The value (in $\text{units}, \textit{round off to two decimal places}$) obtained is ________________
go_editor
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Numerical Methods
Mar 1, 2021
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go_editor
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gatecivil-2021-set2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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GATE Civil 2021 Set 1 | Question: 27
The value of $\int_{0}^{1}\:e^{x}\:dx$ using the trapezoidal rule with four equal subintervals is $1.718$ $1.727$ $2.192$ $2.718$
Arjun
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Numerical Methods
Feb 20, 2021
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Arjun
11.6k
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gatecivil-2021-set1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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3
GATE Civil 2021 Set 1 | Question: 36
The value of abscissa $(x)$ and ordinate $(y)$ ... $1/3^\text{rd}$ rule, the area under the curve $\textit{(round off to two decimal places)}$ is __________________
Arjun
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Numerical Methods
Feb 20, 2021
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Arjun
11.6k
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gatecivil-2021-set1
numerical-answers
numerical-methods
simpsons-rule
integration-by-trapezoidal-and-simpsons-rule
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0
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4
GATE2020 CE-2-3
The integral $\int\limits_{0}^{1} (5x^3 + 4x^2 + 3x + 2) dx$ is estimated numerically using three alternative methods namely the rectangular,trapezoidal and Simpson's rules with a common step size. In this context, which one of the following ... NON-zero error. Only the rectangular rule of estimation will give zero error. Only Simpson's rule of estimation will give zero error.
go_editor
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Numerical Methods
Feb 13, 2020
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go_editor
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gate2020-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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2
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5
GATE2019 CE-2: 43
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \: 1.87$, and $1.15 \:m$. The area (in $m^2$, round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is ________
Arjun
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Numerical Methods
Feb 12, 2019
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Arjun
11.6k
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gate2019-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
numerical-answers
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6
GATE2015-2-29
For step-size, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______. $\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 x^5) dx$
Milicevic3306
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Numerical Methods
Mar 26, 2018
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Milicevic3306
11.9k
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gate2015-ce-2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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7
GATE2015-1-2
The integral $\int_{x_{1}}^{x_{2}}x^{2}\:dx$ with $x_{2}>x_{1}>0$ is evaluated analytically as well as numerically using a single application of the trapezoidal rule. If $I$ is the exact value of the integral obtained analytically and ... , which of the following statement is correct about their relationship? $J>I$ $J<I$ $J=I$ Insufficient data to determine the relationship
Milicevic3306
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Numerical Methods
Mar 26, 2018
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Milicevic3306
11.9k
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gate2015-ce-1
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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8
GATE Civil 2013 | Question: 27
Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s $\dfrac{1}{3}$ Rule. Take the step length as $1$ _________ $\int_0^4 (x^4+10) dx$
Milicevic3306
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Numerical Methods
Mar 26, 2018
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Milicevic3306
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gate2013-ce
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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9
GATE Civil 2012 | Question: 1
The estimate of $\int_{0.5}^{1.5} \dfrac{dx}{x}$ obtained using Simpson’s rule with three-point function evaluation exceeds the exact value by $0.235$ $0.068$ $0.024$ $0.012$
Milicevic3306
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Numerical Methods
Mar 25, 2018
by
Milicevic3306
11.9k
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gate2012-ce
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
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