Question

Use four rectangles to estimate the area between the graph of the function f(x)= 4/11xand the x-axis on the interval[3, 7] using the right endpoints of the subintervals as the sample points. Write the exact answer. Do not round.

Answer 1

First, find the width of the rectangles

7-3 = 4

We ware using 4 rectangles

4/4 =1

delta x = 1

We are using the right side

So the values are at 4,5,6,7

The function evaluated at the right hand side times the width of the rectangle summed for the 4 rectangles

The summation is f(4) *1 + f(5) *1 + f(6) *1 + f(7) *1

4/(11(4)) *1 + 4/(11(5)) *1 + 4/(11(6)) *1 + 4/(11 (7)) *1

4/44 + 4/55 + 4/66 +4/77

29/105