Find the approximated integral value of an equation 1/x using Left endpoint approximation
a = 1 and b = 2
Step value (h) = 0.25Solution:Equation is `f(x)=(1)/(x)`
`a=1`
`b=2`
The value of table for `x` and `f(x)`
| `x` | `f(x)` |
| `x_0=1` | `f(x_(0))=f(1)=1` |
| `x_1=1.25` | `f(x_(1))=f(1.25)=0.8` |
| `x_2=1.5` | `f(x_(2))=f(1.5)=0.6667` |
| `x_3=1.75` | `f(x_(3))=f(1.75)=0.5714` |
| `x_4=2` | `f(x_(4))=f(2)=0.5` |
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+0.8+0.6667+0.5714)`
`=0.25xx(3.0381)`
`=0.7595`
Solution by Left endpoint approximation (Left Riemann Sum) is `0.7595`
This material is intended as a summary. Use your textbook for detail explanation.
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