Estimate the area underneath the curve by evaluating the Rieman sum using 6 rectangles

Split up the interval [0, 4] into 6 subintervals of equal length (4-0)/6 = 2/3:

[0, 2/3], [2/3, 4/3], [4/3, 2], [2, 8/3], [8/3, 10/3], [10/3, 4]

The right endpoints form an arithmetic sequence,

where .

We estimate the area under the curve over each subinterval by a rectangle with length 2/3 and height equal to the value of the function at the right endpoint. Then the value of the integral is approximately equal to the sum of these rectangles' areas:

We have , so

Recall that

answer: y = -2.5x - 15

              (-6,0)

step-by-step explanation:

      2

  2 is to go somewhat to the top right of a because it is squared    

v= a h/3