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