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 :

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step-by-step explanation:

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.