Find the approximated integral value using Left endpoint approximation
| x | f(x) |
| 0.0 | 1.0000 |
| 0.1 | 0.9975 |
| 0.2 | 0.9900 |
| 0.3 | 0.9776 |
| 0.4 | 0.8604 |
Solution:The value of table for `x` and `f(x)`
| `x` | `f(x)` |
| `x_0=0` | `f(x_(0))=1` |
| `x_1=0.1` | `f(x_(1))=0.9975` |
| `x_2=0.2` | `f(x_(2))=0.99` |
| `x_3=0.3` | `f(x_(3))=0.9776` |
| `x_4=0.4` | `f(x_(4))=0.8604` |
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)))`
`=0.1xx(1+0.9975+0.99+0.9776)`
`=0.1xx(3.9651)`
`=0.3965`
Solution by Left endpoint approximation (Left Riemann Sum) is `0.3965`
This material is intended as a summary. Use your textbook for detail explanation.
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