3. Find Solution of an equation x^3-2x+1 using Boole's 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 Boole's Rule
`int y dx=(2h)/45 [7(y_0 + y_4)+32(y_1+y_3)+12(y_2)+14()]`
`int y dx=(2xx0.5)/45 [7xx(5 +57)+32xx(11.625+36.875)+12xx(22)+14xx()]`
`int y dx=(2xx0.5)/45 [7xx(62) + 32xx(48.5) + 12xx(22) + 14xx(0)]`
`int y dx=(2xx0.5)/45 [(434) + (1552) + (264) + (0)]`
`int y dx=50`
Solution by Boole's Rule is `50`
Method-2:Using Boole's Rule
`int y dx=(2h)/45 [7y_0+32y_1+12y_2+32y_3+7y_4]`
`7y_0=7*5=35`
`32y_1=32*11.625=372`
`12y_2=12*22=264`
`32y_3=32*36.875=1180`
`7y_4=7*57=399`
`int y dx=(2xx0.5)/45*(35+372+264+1180+399)`
`int y dx=(2xx0.5)/45*(2250)`
`int y dx=50`
Solution by Boole's Rule is `50`
This material is intended as a summary. Use your textbook for detail explanation.
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