Find the approximated integral value using Left endpoint approximation
| x | f(x) |
| 0.00 | 1.0000 |
| 0.25 | 0.9896 |
| 0.50 | 0.9589 |
| 0.75 | 0.9089 |
| 1.00 | 0.8415 |
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`
This material is intended as a summary. Use your textbook for detail explanation.
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