2. Find Solution of an equation 1/(x+1) using Trapezoidal rule
x1 = 0 and x2 = 1
Interval N = 5Solution:Equation is `f(x)=(1)/(x+1)`.
`h = (b-a)/N`
`h = (1 - 0) / 5 = 0.2`
The value of table for `x` and `y`
| x | 0 | 0.2 | 0.4 | 0.6 | 0.8 | 1 |
|---|
| y | 1 | 0.8333 | 0.7143 | 0.625 | 0.5556 | 0.5 |
|---|
Method-1:Using Trapezoidal Rule
`int y dx=h/2 [y_0+y_5+2(y_1+y_2+y_3+y_4)]`
`int y dx=0.2/2 [1 +0.5 + 2xx(0.8333+0.7143+0.625+0.5556)]`
`int y dx=0.2/2 [1 +0.5 + 2xx(2.7282)]`
`int y dx=0.2/2 [1 +0.5 + 5.4563]`
`int y dx=0.6956`
Solution by Trapezoidal Rule is `0.6956`
Method-2:Using Trapezoidal Rule
`int y dx=h/2 [y_0+2y_1+2y_2+2y_3+2y_4+y_5]`
`y_0=1`
`2y_1=2*0.8333=1.6667`
`2y_2=2*0.7143=1.4286`
`2y_3=2*0.625=1.25`
`2y_4=2*0.5556=1.1111`
`y_5=0.5`
`int y dx=0.2/2*(1+1.6667+1.4286+1.25+1.1111+0.5)`
`int y dx=0.2/2*(6.9563)`
`int y dx=0.6956`
Solution by Trapezoidal Rule is `0.6956`
This material is intended as a summary. Use your textbook for detail explanation.
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