Find the approximated integral value of an equation 2x^3-4x+1 using Midpoint Rule
a = 2 and b = 4
Step value (h) = 0.5

Solution:
Equation is `f(x)=2x^3-4x+1`

`a=2`

`b=4`

The value of table for `x`

`x`

`x_0=2`

`x_1=2.5`

`x_2=3`

`x_3=3.5`

`x_4=4`

Method-1:
Using Midpoint Rule of Riemann Sum


`int f(x) dx=Delta x xx(f((x_0+x_1)/2)+f((x_1+x_2)/2)+f((x_2+x_3)/2)+f((x_3+x_4)/2))`

`=Delta x xx(f((2+2.5)/2)+f((2.5+3)/2)+f((3+3.5)/2)+f((3.5+4)/2))`

`=Delta x xx(f(2.25)+f(2.75)+f(3.25)+f(3.75))`

`=0.5xx(14.7812+31.5938+56.6562+91.4688)`

`=0.5xx(194.5)`

`=97.25`

Solution by Midpoint Rule of Riemann Sum is `97.25`

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