Calculus question

Question

Approximate the area under the curve y= x³ from x=0 to x=3 using a Right Endpoint approximation with 6 subdivisions.

Answer 1

Six equal subdivisions means that the width of each rectangle would be 3/6 or 0.5 since the entire interval is 3.

For the height of each rectangle, you want to go with the right endpoint. So you would start with f(0.5), then f(1), f(1.5), and so on until you reach f(3).

So adding up the areas of each rectangle looks like this, using width times height:

(0.5)(0.5)^3 + (0.5)(1)^3 + (0.5)(1.5)^3 + (0.5)(2)^3 + (0.5)(2.5)^3 + (0.5)(3)^3

or you can factor out the common width of 0.5 and get

(0.5) [(0.5)^3 + (1)^3 + (1.5)^3 + (2)^3 + (2.5)^3 + (3)^3]