Approximating area

Question

Estimate the area under the graph of y=7x for x between 0 and 2. Use a partition that consists of 4 equal subintervals of [0, 2] and use the left endpoint of each subinterval as a sample point.
The approximating area is____

Answer 1

Given equation of a graph of y=7x to estimate are under it for 0<x<2 

Using partition that consists of 4 equal sub-intervals of [0, 2], Δx=1/4=0.25

x_i     | x=0   | x=0.5  | x= 1| x= 1.5| x=2

y=7x| 0       |  3.5     | 7     | 10.5   | 14

 

Using the left endpoint of each sub-interval as a sample point, estimate the area under the graph of y=7x for x between 0 and 

=y_x=0. Δx + y_x=0.5. Δx + y_x=1. Δx + y_x=1.5. Δx

=0*0.25 + 3.5*0.25 + 7*0.25 + 10.5*0.25

=(3.5 + 7 + 10.5)*0.25

=21*0.25

=5.25