Question

College Math! Pls help

Answer 1

Answer:

right: 11.15

left: 17.15

Step-by-step explanation:

right formula: $\int _a^bf\left(x\right)dx\:\approx \Delta \:x\left(f\left(x_1\right)+f\left(x_2\right)+...+f\left(x_n\right)\right)$

left formula: $\int _a^bf\left(x\right)dx\:\approx \Delta \:x\left(f\left(x_0\right)+f\left(x_1\right)+...+f\left(x_{n-1}\right)\right),$

$\Delta \:x\:=\:\frac{b-a}{n}$

estimating : $\int _1^7\left(\frac{7}{x}\right)dx$ , with n = 6 (number of sub-intervals in Riemann sum)

right: 1 $\left(f\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)+f\left(x_4\right)+f\left(x_5\right)+f\left(x_6\right)\right)$ =$1\cdot \left(\frac{7}{2}+\frac{7}{3}+\frac{7}{4}+\frac{7}{5}+\frac{7}{6}+1\right)$ = 11.5

left: $1\cdot \left(f\left(x_0\right)+f\left(x_1\right)+f\left(x_2\right)+f\left(x_3\right)+f\left(x_4\right)+f\left(x_5\right)\right)$ =

$1\cdot \left(7+\frac{7}{2}+\frac{7}{3}+\frac{7}{4}+\frac{7}{5}+\frac{7}{6}\right)$ = 17.15