|
Q. 3. Compute the approximate value of the
integral (June 2001)
I = (x
+ x2) dx
using Simpson's rule by taking interval size h as
1.
Solution.
| x
|
-1 |
0 |
1
|
| y
= (x + x2) |
0 |
0 |
2
|
Here, h = 1, y0 = 0, y1 =
0, y2 = 2
y
dx = (1/3) X [(0 + 2) + (4 X 0)]
ory
dx = 2/3
Q. 4. Compute the approximate value of the
integral (Dec. 2000)
I = [1/(1
+ x2)] dx
using Simpson's rule by taking interval size h as
1.
Solution.
| x
|
0 |
1 |
2
|
3
|
4
|
5
|
6 |
| y
= [1/(1 + x2)] |
1 |
0.5 |
0.2
|
0.1
|
0.058
|
0.038
|
0.027
|
y
dx = (1/3) X {(1 + 0.027) + [4 X (0.5 + 0.1 + 0.038)]
+ [2 X (0.2 + 0.058)]}
or y
dx = 1.36
|
