Find the approximated integral value using Simpson's 3/8 rule
| x | f(x) |
| 0.00 | 1.0000 |
| 0.25 | 0.9896 |
| 0.50 | 0.9589 |
| 0.75 | 0.9089 |
| 1.00 | 0.8415 |
Solution:The value of table for `x` and `f(x)`
| `x` | `f(x)` |
| `x_0=0` | `f(x_(0))=1` |
| `x_1=0.25` | `f(x_(1))=0.9896` |
| `x_2=0.5` | `f(x_(2))=0.9589` |
| `x_3=0.75` | `f(x_(3))=0.9089` |
| `x_4=1` | `f(x_(4))=0.8415` |
Method-1:Using Simpson's `3/8` Rule
`int f(x) dx=(3Delta x )/8 (f(x_(0))+2(f(x_(3))+f(x_(3))+...+f(x_(n-3)))+3(f(x_(1))+f(x_(2))+f(x_(4))+f(x_(5))+...+f(x_(2))+f(x_(n-1)))+f(x_(n)))`
`int f(x) dx=(3Delta x )/8 [f(x_(0))+3f(x_(1))+3f(x_(2))+2f(x_(3))+f(x_(4))]`
`f(x_(0))=1`
`3f(x_(1))=3*0.9896=2.9688`
`3f(x_(2))=3*0.9589=2.8767`
`2f(x_(3))=2*0.9089=1.8178`
`f(x_(4))=0.8415`
`int f(x) dx=(3xx0.25)/8 *(1+2.9688+2.8767+1.8178+0.8415)`
`=(3xx0.25)/8 *(9.5048)`
`=0.8911`
Solution by Simpson's `3/8` Rule is `0.8911`
Method-2:Using Simpson's `3/8` Rule
`int f(x) dx=(3Delta x )/8 (f(x_(0))+2(f(x_(3))+f(x_(3))+...+f(x_(n-3)))+3(f(x_(1))+f(x_(2))+f(x_(4))+f(x_(5))+...+f(x_(2))+f(x_(n-1)))+f(x_(n)))`
`int f(x) dx=(3Delta x )/8 [(f(x_(0))+f(x_(4)))+2(f(x_(3)))+3(f(x_(1))+f(x_(2)))]`
`=(3xx0.25)/8 [(1 +0.8415)+2xx(0.9089)+3xx(0.9896+0.9589)]`
`=(3xx0.25)/8 [(1 +0.8415)+2xx(0.9089)+3xx(1.9485)]`
`=(3xx0.25)/8 [(1.8415)+(1.8178)+(5.8455)]`
`=0.8911`
Solution by Simpson's `3/8` Rule is `0.8911`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
