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4. Left endpoint approximation example ( Enter your problem )
  1. Formula & Example-1 (table data)
  2. Example-2 (table data)
  3. Example-3 (table data)
  4. Example-4 `(f(x)=1/x)`
  5. Example-5 `(f(x)=1/(x+1))`
  6. Example-6 `(f(x)=x^3-2x+1)`
  7. Example-7 `(f(x)=2x^3-4x+1)`
Other related methods
  1. Left Riemann Sum
  2. Right Riemann Sum
  3. Midpoint Rule of Riemann Sum
  4. Left endpoint approximation
  5. Right endpoint approximation
  6. Trapezoidal rule
  7. Simpson's 1/3 rule
  8. Simpson's 3/8 rule
  9. Boole's rule
  10. Weddle's rule

2. Example-2 (table data)
(Previous example)
4. Example-4 `(f(x)=1/x)`
(Next example)

3. Example-3 (table data)





Find the approximated integral value using Left endpoint approximation
xf(x)
0.001.0000
0.250.9896
0.500.9589
0.750.9089
1.000.8415


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

`x``f(x)`
`x_0=0``f(x_(0))=1`
`x_1=0.25``f(x_(1))=0.9896`
`x_2=0.5``f(x_(2))=0.9589`
`x_3=0.75``f(x_(3))=0.9089`
`x_4=1``f(x_(4))=0.8415`


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_(n-1)))`


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

`=0.25xx(1+0.9896+0.9589+0.9089)`

`=0.25xx(3.8574)`

`=0.9644`

Solution by Left endpoint approximation (Left Riemann Sum) is `0.9644`




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2. Example-2 (table data)
(Previous example)
4. Example-4 `(f(x)=1/x)`
(Next example)





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