4. Find Solution of an equation 2x^3-4x+1 using Boole's rule
x1 = 2 and x2 = 4
Step value (h) = 0.5Solution:Equation is `f(x)=2x^3-4x+1`.
The value of table for `x` and `y`
| x | 2 | 2.5 | 3 | 3.5 | 4 |
|---|
| y | 9 | 22.25 | 43 | 72.75 | 113 |
|---|
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(9 +113)+32xx(22.25+72.75)+12xx(43)+14xx()]`
`int y dx=(2xx0.5)/45 [7xx(122) + 32xx(95) + 12xx(43) + 14xx(0)]`
`int y dx=(2xx0.5)/45 [(854) + (3040) + (516) + (0)]`
`int y dx=98`
Solution by Boole's Rule is `98`
Method-2:Using Boole's Rule
`int y dx=(2h)/45 [7y_0+32y_1+12y_2+32y_3+7y_4]`
`7y_0=7*9=63`
`32y_1=32*22.25=712`
`12y_2=12*43=516`
`32y_3=32*72.75=2328`
`7y_4=7*113=791`
`int y dx=(2xx0.5)/45*(63+712+516+2328+791)`
`int y dx=(2xx0.5)/45*(4410)`
`int y dx=98`
Solution by Boole's Rule is `98`
This material is intended as a summary. Use your textbook for detail explanation.
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