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GATE Mechanical 2014 Set 1 | Question: 29
Arjun
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Numerical Methods
Feb 19, 2017
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Mar 4, 2021
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Lakshman Patel RJIT
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Using the trapezoidal rule, and dividing the interval of integration into three equal subintervals, the definite integral $\int_{-1}^{+1} \mid x \mid dx$ is _____
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Arjun
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Numerical Methods
Feb 19, 2017
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Lakshman Patel RJIT
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Answer:
1.10 : 1.12
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Arjun
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GATE Mechanical 2014 Set 2 | Question: 29
The value of $\int_{2.5}^{4} \ln(x)dx$ calculated using the Trapezoidal rule with five subintervals is _______
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Feb 19, 2017
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Feb 24, 2017
GATE2016-1-29
Gauss-Seidel method is used to solve the following equations (as per the given order): $x_1+2x_2+3x_3=5$ $2x_1+3x_2+x_3=1$ $3x_1+2x_2+x_3=3$ Assuming initial guess as $x_1=x_2=x_3=0$ , the value of $x_3$ after the first iteration is __________
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Feb 24, 2017
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Arjun
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Arjun
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Feb 24, 2017
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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 ___________
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Feb 24, 2017
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Arjun
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Arjun
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Feb 24, 2017
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 __________
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Feb 24, 2017
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Arjun
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Feb 19, 2017
GATE Mechanical 2014 Set 4 | Question: 29
Consider an ordinary differential equation $\dfrac{dx}{dt}=4t+4$. If $x = x_0$ at $t = 0$, the increment in $x$ calculated using Runge-Kutta fourth order multi-step method with a step size of $\Delta t = 0.2$ is $0.22$ $0.44$ $0.66$ $0.88$
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