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5. Right 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

4. Example-4 `(f(x)=1/x)`
(Previous example)
6. Example-6 `(f(x)=x^3-2x+1)`
(Next example)

5. Example-5 `(f(x)=1/(x+1))`





Find the approximated integral value of an equation 1/(x+1) using Right endpoint approximation
a = 0 and b = 1
Interval n = 5


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

`a=0`

`b=1`

`Delta x =(b-a)/n=(1 - 0)/5=0.2`

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

`x``f(x)`
`x_0=0``f(x_(0))=f(0)=1`
`x_1=0.2``f(x_(1))=f(0.2)=0.8333`
`x_2=0.4``f(x_(2))=f(0.4)=0.7143`
`x_3=0.6``f(x_(3))=f(0.6)=0.625`
`x_4=0.8``f(x_(4))=f(0.8)=0.5556`
`x_5=1``f(x_(5))=f(1)=0.5`


Method-1:
Using Right endpoint approximation (Right Riemann Sum)
`int f(x) dx=Delta x xx(f(x_(1))+f(x_(2))+...+f(x_(n)))`


`int f(x) dx=Delta x xx(f(x_(1))+f(x_(2))+f(x_(3))+f(x_(4))+f(x_(5)))`

`=0.2xx(0.8333+0.7143+0.625+0.5556+0.5)`

`=0.2xx(3.2282)`

`=0.6456`

Solution by Right endpoint approximation (Right Riemann Sum) is `0.6456`




This material is intended as a summary. Use your textbook for detail explanation.
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4. Example-4 `(f(x)=1/x)`
(Previous example)
6. Example-6 `(f(x)=x^3-2x+1)`
(Next example)





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