Formula

1. Left endpoint approximation `int y dx=h (y_0+y_1+y_2+ ... + y_(n-1))` `int f(x) dx=Delta x xx(f(x_(0))+f(x_(1))+f(x_(2))+...+f(x_(n-1)))`

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Examples
1. Find the approximated integral value using Left endpoint approximation

x	f(x)
1.4	4.0552
1.6	4.9530
1.8	6.0436
2.0	7.3891
2.2	9.0250

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

`x`	`f(x)`
`x_0=1.4`	`f(x_(0))=4.0552`
`x_1=1.6`	`f(x_(1))=4.953`
`x_2=1.8`	`f(x_(2))=6.0436`
`x_3=2`	`f(x_(3))=7.3891`
`x_4=2.2`	`f(x_(4))=9.025`

Method-1:
Using Left endpoint approximation (Left Riemann Sum)


`int f(x) dx=Delta x xx(f(x_(0))+f(x_(1))+f(x_(2))+f(x_(3)))`

`=0.2xx(4.0552+4.953+6.0436+7.3891)`

`=0.2xx(22.4409)`

`=4.4882`

Solution by Left endpoint approximation (Left Riemann Sum) is `4.4882`

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