Find the approximated integral value of an equation 1/x using Midpoint Rule
a = 1 and b = 2
Step value (h) = 0.25

Solution:
Equation is `f(x)=(1)/(x)`

`a=1`

`b=2`

The value of table for `x`

`x`

`x_0=1`

`x_1=1.25`

`x_2=1.5`

`x_3=1.75`

`x_4=2`

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((1+1.25)/2)+f((1.25+1.5)/2)+f((1.5+1.75)/2)+f((1.75+2)/2))`

`=Delta x xx(f(1.125)+f(1.375)+f(1.625)+f(1.875))`

`=0.25xx(0.8889+0.7273+0.6154+0.5333)`

`=0.25xx(2.7649)`

`=0.6912`

Solution by Midpoint Rule of Riemann Sum is `0.6912`

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