Answer:
right: 11.15
left: 17.15
Step-by-step explanation:
right formula: [tex]\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)[/tex]
left formula: [tex]\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),[/tex]
[tex]\Delta \:x\:=\:\frac{b-a}{n}[/tex]
estimating : [tex]\int _1^7\left(\frac{7}{x}\right)dx[/tex] , with n = 6 (number of sub-intervals in Riemann sum)
right: 1 [tex]\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)[/tex] =[tex]1\cdot \left(\frac{7}{2}+\frac{7}{3}+\frac{7}{4}+\frac{7}{5}+\frac{7}{6}+1\right)[/tex] = 11.5
left: [tex]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)[/tex] =
[tex]1\cdot \left(7+\frac{7}{2}+\frac{7}{3}+\frac{7}{4}+\frac{7}{5}+\frac{7}{6}\right)[/tex] = 17.15
