3. Find Solution of an equation x^3-2x+1 using Trapezoidal rule
x1 = 2 and x2 = 4
Step value (h) = 0.5Solution:Equation is `f(x)=x^3-2x+1`.
The value of table for `x` and `y`
| x | 2 | 2.5 | 3 | 3.5 | 4 |
|---|
| y | 5 | 11.625 | 22 | 36.875 | 57 |
|---|
Method-1:Using Trapezoidal Rule
`int y dx=h/2 [y_0+y_4+2(y_1+y_2+y_3)]`
`int y dx=0.5/2 [5 +57 + 2xx(11.625+22+36.875)]`
`int y dx=0.5/2 [5 +57 + 2xx(70.5)]`
`int y dx=0.5/2 [5 +57 + 141]`
`int y dx=50.75`
Solution by Trapezoidal Rule is `50.75`
Method-2:Using Trapezoidal Rule
`int y dx=h/2 [y_0+2y_1+2y_2+2y_3+y_4]`
`y_0=5`
`2y_1=2*11.625=23.25`
`2y_2=2*22=44`
`2y_3=2*36.875=73.75`
`y_4=57`
`int y dx=0.5/2*(5+23.25+44+73.75+57)`
`int y dx=0.5/2*(203)`
`int y dx=50.75`
Solution by Trapezoidal Rule is `50.75`
This material is intended as a summary. Use your textbook for detail explanation.
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