3. Find Solution using Trapezoidal 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 `y`
| x | 0 | 0.25 | 0.5 | 0.75 | 1 |
|---|
| y | 1 | 0.9896 | 0.9589 | 0.9089 | 0.8415 |
|---|
Method-1:Using Trapezoidal Rule
`int y dx=h/2 [y_0+y_4+2(y_1+y_2+y_3)]`
`int y dx=0.25/2 [1 +0.8415 + 2xx(0.9896+0.9589+0.9089)]`
`int y dx=0.25/2 [1 +0.8415 + 2xx(2.8574)]`
`int y dx=0.25/2 [1 +0.8415 + 5.7148]`
`int y dx=0.9445`
Solution by Trapezoidal Rule is `0.9445`
Method-2:Using Trapezoidal Rule
`int y dx=h/2 [y_0+2y_1+2y_2+2y_3+y_4]`
`y_0=1`
`2y_1=2*0.9896=1.9792`
`2y_2=2*0.9589=1.9178`
`2y_3=2*0.9089=1.8178`
`y_4=0.8415`
`int y dx=0.25/2*(1+1.9792+1.9178+1.8178+0.8415)`
`int y dx=0.25/2*(7.5563)`
`int y dx=0.9445`
Solution by Trapezoidal Rule is `0.9445`
This material is intended as a summary. Use your textbook for detail explanation.
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