1. Find Solution of an equation 1/x using Trapezoidal rule
x1 = 1 and x2 = 2
Step value (h) = 0.25Solution:Equation is `f(x)=(1)/(x)`.
The value of table for `x` and `y`
| x | 1 | 1.25 | 1.5 | 1.75 | 2 |
|---|
| y | 1 | 0.8 | 0.6667 | 0.5714 | 0.5 |
|---|
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 +0.5 + 2xx(0.8+0.6667+0.5714)]`
`int y dx=0.25/2 [1 +0.5 + 2xx(2.0381)]`
`int y dx=0.25/2 [1 +0.5 + 4.0762]`
`int y dx=0.697`
Solution by Trapezoidal Rule is `0.697`
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*0.8=1.6`
`2y_2=2*0.6667=1.3333`
`2y_3=2*0.5714=1.1429`
`y_4=0.5`
`int y dx=0.25/2*(1+1.6+1.3333+1.1429+0.5)`
`int y dx=0.25/2*(5.5762)`
`int y dx=0.697`
Solution by Trapezoidal Rule is `0.697`
This material is intended as a summary. Use your textbook for detail explanation.
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