Approximate the area under the curve

Question

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

Answer 1

You want to use 6 rectangles.  Now you need to find the length of the base of each rectangle.

 

length of base = (6 - 3) / 6 = 3/6 = 0.5

 

For the 1st rectangle: area = 0.5 * f(3.5)

For the 2nd rectangle: area = 0.5 * f(4)

For the 3rd rectangle:  area = 0.5 * f(4.5)

For the 4th rectangle:  area = 0.5 * f(5)

For the 5th rectangle:  area = 0.5 * f(5.5)

For the 6th rectangle:  area = 0.5 * f(6)

 

Add up these 6 areas the get the area under the curve.