Question

College Math! Pls help

Answer 1

right: 11.15

left: 17.15

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\:=\:(b-a)/(n)`

estimating :
`\int _1^7\left((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((7)/(2)+(7)/(3)+(7)/(4)+(7)/(5)+(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+(7)/(2)+(7)/(3)+(7)/(4)+(7)/(5)+(7)/(6)\right)` = 17.15