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If the trapezoidal method is used to evaluate the integral obtained $\int_{0}^{1} x^2dx$, then the value obtained is always > (1/3) is always < (1/3) is always = (1/3) may be greater or lesser than (1/3)
asked Nov 3, 2014 in Numerical Methods Ishrat Jahan 438 views
0 votes
1 answer
2
The trapezoidal method is used to evaluate the numerical value of $\int_{0}^{1}e^x dx$. Consider the following values for the step size h. 10-2 10-3 10-4 10-5 For which of these values of the step size h, is the computed value guaranteed to be correct to seven decimal places. Assume that there are no round-off errors in the computation. iv only iii and iv only ii, iii and iv only i, ii, iii and iv
asked Oct 30, 2014 in Numerical Methods Ishrat Jahan 544 views
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1 answer
3
Is the value obtained by trapezoidal rule greater than the exact value and also compare the value obtained in the case of simpsons rule.
asked Oct 26, 2014 in Numerical Methods kireeti 153 views
0 votes
1 answer
4
The trapezoidal method to numerically obtain $\int_a^b f(x) dx$ has an error E bounded by $\frac{b-a}{12} h^2 \max f&rsquo;&rsquo;(x), x \in [a, b]$ where $h$ is the width of the trapezoids. The minimum number of trapezoids guaranteed to ensure $E \leq 10^{-4}$ in computing $\ln 7$ using $f=\frac{1}{x}$ is 60 100 600 10000
asked Sep 29, 2014 in Numerical Methods Kathleen 440 views
5 votes
1 answer
5
With respect to the numerical evaluation of the definite integral, $K = \int \limits_a^b \:x^2 \:dx$, where $a$ and $b$ are given, which of the following statements is/are TRUE? The value of $K$ obtained using the trapezoidal rule is always greater than or equal ... using the Simpson's rule is always equal to the exact value of the definite integral. I only II only Both I and II Neither I nor II
asked Sep 28, 2014 in Numerical Methods jothee 1.3k views
2 votes
2 answers
6
Function $f$ is known at the following points: $x$ 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3.0 $f(x)$ 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 7.29 9.00 The value of $\int_{0}^{3} f(x) \text{d}x$ computed using the trapezoidal rule is (A) 8.983 (B) 9.003 (C) 9.017 (D) 9.045
asked Sep 24, 2014 in Numerical Methods Arjun 1.2k views
1 vote
1 answer
7
The trapezoidal rule for integration gives exact result when the integrand is a polynomial of degree 0 but not 1 1 but not 0 0 or 1 2
asked Sep 15, 2014 in Numerical Methods Kathleen 1k views
1 vote
2 answers
8
The minimum number of equal length subintervals needed to approximate $\int_1^2 xe^x\,dx$ to an accuracy of at least $\frac{1}{3}\times10^{-6}$ using the trapezoidal rule is 1000e 1000 100e 100
asked Sep 12, 2014 in Numerical Methods Kathleen 991 views
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