Approximating the area

Question

Estimate the area under the graph of y=x2+6x for x between 0 and 2. Use a partition that consists of 4 equal subintervals of [0, 2] and use the right endpoint of each subinterval as a sample point.
The approximating area is___

Answer 1

Given equation of a graph of y=x²+6x 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=x²+6x| 0     | 3.25     | 7     | 11.25| 16

Using the right endpoint of each sub-interval as a sample point, estimate the area under the graph of y=x²+6 for x between 0 and 2
= y_x=0.5. Δx + y_x=1. Δx + y_x=1.5. Δx + y_x=2. Δx
=3.25*0.25 + 7*0.25 + 11.25*0.25 + 16*0.25
=(3.25 + 7 + 11.25+16)*0.25
=37.5*0.25
=9.375