Estimate the area under the graph of f(x)=2x^2-12x+22 over the interval [0,2] using four approximating rectangles and right endpoints.

The right Riemann sum is 21.5.

The left Riemann sum is 29.5.

Step-by-step explanation:

The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a sub-interval:

, where .

To find the Riemann sum for with 4 rectangles, using right endpoints you must:

We have that a = 0, b = 2, n = 4. Therefore, .

Divide the interval [0,2] into n = 4 sub-intervals of length :

Now, we just evaluate the function at the right endpoints:

Finally, just sum up the above values and multiply by :

The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a sub-interval:

, where .

To find the Riemann sum for with 4 rectangles, using left endpoints you must:

We have that a = 0, b = 2, n = 4. Therefore, .

Divide the interval [0,2] into n = 4 sub-intervals of length :

Now, we just evaluate the function at the left endpoints:

Finally, just sum up the above values and multiply by :

answer: 1 and 3

step-by-step explanation:

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew