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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

6. Example-6 `(f(x)=x^3-2x+1)`
(Previous example)
5. Right endpoint approximation
(Next method)

7. Example-7 `(f(x)=2x^3-4x+1)`





Find the approximated integral value of an equation 2x^3-4x+1 using Left endpoint approximation
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` and `f(x)`

`x``f(x)`
`x_0=2``f(x_(0))=f(2)=9`
`x_1=2.5``f(x_(1))=f(2.5)=22.25`
`x_2=3``f(x_(2))=f(3)=43`
`x_3=3.5``f(x_(3))=f(3.5)=72.75`
`x_4=4``f(x_(4))=f(4)=113`


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)))`

`=0.5xx(9+22.25+43+72.75)`

`=0.5xx(147)`

`=73.5`

Solution by Left endpoint approximation (Left Riemann Sum) is `73.5`




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6. Example-6 `(f(x)=x^3-2x+1)`
(Previous example)
5. Right endpoint approximation
(Next method)





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