use the tabulated values of f to evaluate the left and right riemann sums for n = 10 over the interval…

use the tabulated values of f to evaluate the left and right riemann sums for n = 10 over the interval 0,5.\n| x | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |\n| f(x) | 3 | 5 | 11 | 18 | 24 | 36 | 26 | 15 | 8 | 4 | 1 |\nthe left riemann sum is \n(simplify your answer.)

use the tabulated values of f to evaluate the left and right riemann sums for n = 10 over the interval 0,5.\n| x | 0 | 0.5 | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 |\n| f(x) | 3 | 5 | 11 | 18 | 24 | 36 | 26 | 15 | 8 | 4 | 1 |\nthe left riemann sum is \n(simplify your answer.)

Answer

Explanation:

Step1: Determine the width of sub - intervals

The interval is $[0,5]$ and $n = 10$. The width of each sub - interval $\Delta x=\frac{5 - 0}{10}=0.5$.

Step2: Calculate the left Riemann sum

The left Riemann sum $L_{10}=\sum_{i = 0}^{9}f(x_i)\Delta x$. We have $\Delta x = 0.5$, and $f(x_0)=3,f(x_1)=5,f(x_2)=11,f(x_3)=18,f(x_4)=24,f(x_5)=36,f(x_6)=26,f(x_7)=15,f(x_8)=8,f(x_9)=4$. $L_{10}=0.5\times(3 + 5+11+18+24+36+26+15+8+4)$ $=0.5\times140$ $ = 70$

Answer:

70