2. Find Solution using Trapezoidal rule
| x | f(x) |
| 0.0 | 1.0000 |
| 0.1 | 0.9975 |
| 0.2 | 0.9900 |
| 0.3 | 0.9776 |
| 0.4 | 0.8604 |
Solution:The value of table for `x` and `y`
| x | 0 | 0.1 | 0.2 | 0.3 | 0.4 |
|---|
| y | 1 | 0.9975 | 0.99 | 0.9776 | 0.8604 |
|---|
Method-1:Using Trapezoidal Rule
`int y dx=h/2 [y_0+y_4+2(y_1+y_2+y_3)]`
`int y dx=0.1/2 [1 +0.8604 + 2xx(0.9975+0.99+0.9776)]`
`int y dx=0.1/2 [1 +0.8604 + 2xx(2.9651)]`
`int y dx=0.1/2 [1 +0.8604 + 5.9302]`
`int y dx=0.3895`
Solution by Trapezoidal Rule is `0.3895`
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*0.9975=1.995`
`2y_2=2*0.99=1.98`
`2y_3=2*0.9776=1.9552`
`y_4=0.8604`
`int y dx=0.1/2*(1+1.995+1.98+1.9552+0.8604)`
`int y dx=0.1/2*(7.7906)`
`int y dx=0.3895`
Solution by Trapezoidal Rule is `0.3895`
This material is intended as a summary. Use your textbook for detail explanation.
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