4. Find Solution of an equation 2x^3-4x+1 using Trapezoidal 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 Trapezoidal Rule
`int y dx=h/2 [y_0+y_4+2(y_1+y_2+y_3)]`
`int y dx=0.5/2 [9 +113 + 2xx(22.25+43+72.75)]`
`int y dx=0.5/2 [9 +113 + 2xx(138)]`
`int y dx=0.5/2 [9 +113 + 276]`
`int y dx=99.5`
Solution by Trapezoidal Rule is `99.5`
Method-2:Using Trapezoidal Rule
`int y dx=h/2 [y_0+2y_1+2y_2+2y_3+y_4]`
`y_0=9`
`2y_1=2*22.25=44.5`
`2y_2=2*43=86`
`2y_3=2*72.75=145.5`
`y_4=113`
`int y dx=0.5/2*(9+44.5+86+145.5+113)`
`int y dx=0.5/2*(398)`
`int y dx=99.5`
Solution by Trapezoidal Rule is `99.5`
This material is intended as a summary. Use your textbook for detail explanation.
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