Question

use four rectangles to estimate the area between the graph of the function and the x-axis on the interval using the right endpoints of the subintervals as the sample points

Answer 1

we have the function

f(x)=6/(7x)

the interval [2,6]

Divide into fur rectangles

the width of each rectangle is equal to

(6-2)/4=1

the intervals are

(2,3) (3,4) (4,5) and (5,6)

using the right endpoints

the approximate area is equal to

A1=f(3)*(1)=[6/(7*3)]*(1)=6/21

A2=f(4)*(1)=[6/(7*4)]*(1)=6/28

A3=f(5)*(1)=[6/(7*5)]*(1)=6/35

A4=f(6)*(1)=[6/(7*6)]*(1)=6/42

therefore

the approximate area is

A=(6/21)+((6/28)+(6/35)+(6/42)

simplify

A=(6/7)*[(1/3)+(1/4)+(1/5)+(1/6)]

A=(6/7)*[(20+15+12+10)/60]

A=(6/7)*[57/60]

A=57/70 unit2 -----> exact answer