Answer:
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 :