Find the approximated integral value of an equation 2x^3-4x+1 using Left endpoint approximation
a = 2 and b = 4
Step value (h) = 0.5Solution:Equation is `f(x)=2x^3-4x+1`
`a=2`
`b=4`
The value of table for `x` and `f(x)`
| `x` | `f(x)` |
| `x_0=2` | `f(x_(0))=f(2)=9` |
| `x_1=2.5` | `f(x_(1))=f(2.5)=22.25` |
| `x_2=3` | `f(x_(2))=f(3)=43` |
| `x_3=3.5` | `f(x_(3))=f(3.5)=72.75` |
| `x_4=4` | `f(x_(4))=f(4)=113` |
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)))`
`=0.5xx(9+22.25+43+72.75)`
`=0.5xx(147)`
`=73.5`
Solution by Left endpoint approximation (Left Riemann Sum) is `73.5`
This material is intended as a summary. Use your textbook for detail explanation.
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