Page 226 - Engineering Mathematics Workbook_Final

Numerical Methods

1.5
94. The estimate of  dx obtained using 98. The accuracy of Simpson’s rule
0.5 x quadrature for a step size h is

Simpson’s rule with three-point 2 3
O h
O h
function evaluation exceeds the exact (a) ( ) (b) ( )
value by
4
5
O h
O h
(c) ( ) (d) ( )
(a) 0.235 (b) 0.068
[GATE-2003]
(c) 0.024 (d) 0.012
99. Match the correct pairs
[GATE-2012-CE]
Numerical integration Order of Fitting
95. Find the magnitude of the error scheme Polynomial
(correct to two decimal places) in the P. Simpson’s 3/8 Rule 1. First
estimation of following integral using Q. Trapezoidal Rule 2. Second
Simpson’s 1/3 Rule. Take the step R. Simpson’s 1/3 Rule 3. Third
length as 1. ______ (a) P – 2, Q – 1, R – 3
(b) P – 3, Q – 2, R - 1
4
 4 ( x + 10 ) dx (c) P – 1, Q – 2, R – 3
0
(d) P – 3, Q – 1, R – 2
[GATE-2013-CE]
[GATE-2013-ME]

96. For step-size; x = 0.4 the value of 2 x 2
the following integral 100. The integral 1 x  x dx with
x  2 x  1 0 is evaluated analytically
 0.8 (0.2 25x − 200x + 675x − 900x + 400x 5 ) dx as well as numerically using a single
+
4
2
3
0
using Simpson’s 1/3 rule is ____. value of the integral obtained
analytically and J is the approximate
[GATE-2015-CE-SET II] value obtained using the trapezoidal
97. Simpson’s 1/3 rule is used to rule, which of the following
integrate the function statements is correct about their
3 9 relationship?
f ( ) x = x + 2 between x = 0 and
5 5 (a) J > 1

x = 1 using the least number of equal (b) J < 1
sub intervals. The value of integral is

______. (c) J = 1

[GATE-2015-ME-SET 1] (d) Insufficient data to determine the
relationship

[GATE-2015-CE-SET I]

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