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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

use four rectangles to estimate the area between the graph of the function and the xaxis on the interval using the right endpoints of the subintervals as the sa class=

Respuesta :

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