Find the approximated integral value using Midpoint Rule

x	f(x)
0.0	1.0000
0.1	0.9975
0.2	0.9900
0.3	0.9776
0.4	0.8604

Solution:
The value of table for `x` and `f(x)`

`x`	`f(x)`
`x_0=0`	`f(x_(0))=1`
`x_1=0.1`	`f(x_(1))=0.9975`
`x_2=0.2`	`f(x_(2))=0.99`
`x_3=0.3`	`f(x_(3))=0.9776`
`x_4=0.4`	`f(x_(4))=0.8604`

Method-1:
Using Midpoint Rule of Riemann Sum
`int f(x) dx=Delta x xx(f((x_2+x_0)/2)+f((x_4+x_2)/2))`

`=0.2xx(f((0.2+0)/2)+f((0.4+0.2)/2))`

`=0.2xx(f(0.1)+f(0.3))`

`=0.2xx(0.9975+0.9776)`

`=0.2xx(1.9751)`

`=0.1975`

Solution by Midpoint Rule of Riemann Sum is `0.1975`

---

---