Page 218 - Engineering Mathematics Workbook_Final

Numerical Methods

49. Using a unit step size, the value of
integral 1  2 x ln x dx by trapezoidal
x f(x) f   2 f  3 f rule is ________.
- -
0.4 1.7648 0.2965 0.089 -0.03 [GATE 2015 – ME – SET-3]
- - -
0.3 1.4683 0.2075 0.059 0.0228 50. The integral x  x 2 x dx with
2
- - - 1
0.2 1.2608 0.1485 0.0362 0.0156 x  2 x  1 0 is evaluated analytically
- - -
0.1 1.1123 0.1123 0.0206 0.0084 as well as numerically using a single
- - application of the trapezoidal rule. If I
0 1 0.0122
0.0917 0.0012 is the exact value of the integral
- obtained analytically and J is the
0.1 0.9083 0.011 0.006
0.0795
approximate value obtained using the
0.2 0.8288 0.0685 0.017 0.0132
trapezoidal rule, which of the
following statements is correct about

(a) 1 (b) 2 their relationship?

(c) 3 (d) 4 (a) J > I

[GATE 2017 (IN)] (b) J < I


47. For step-size: x = 0.4 the value of (c) J = I
the following integral (d) Insufficient data to determine the

0.8
 (0.2 25x − 200x + 675x − 900x + 400x 5 relationship
+
2
3
4
) dx
0
using Simpson’s 1/3 rule is _______. [GATE 2015 – CE – SET-1]
51. The values of function f(x) at 5
[GATE 2015 – CE – SET-2]
discrete points are given below.
48. Simpson’s 1/3 rule is used to
integrate the function x 0 0.1 0.2 0.3 0.4
3 9 f(x) 0 10 40 90 160
f ( ) x = x + 2 between x = 0 and
5 5 Using Trapezoidal rule with step size

0.4
x = 1 using the least number of equal of 0.1 the value of  f ( ) x dx
sub intervals. The value of integral is 0
___________. _________.

[GATE 2015 – ME – SET-1] [GATE 2015 – ME – SET-2]

52. In numerical integration using
Simpson’s rule, the approximating
function in the interval is a

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