Question

For the function given below, find a formula for the Riemann sum obtained by dividing the interval [a,b] into n equal subintervals and using the right-hand endpoint for each

c Subscript kck.

Then take a limit of this sum as

n right arrow infinityn → ∞

to calculate the area under the curve over [a,b].

f(x)equals=44x

over the interval

[00,44].

Find a formula for the Riemann sum.

Answer #1

Use a graphing calculator Riemann Sum (found here) to
find the following Riemann sums.
f(x) =
2/x
from a = 1 to b =
5
(a) Calculate the Riemann sum for the function for the following
values of n: 10, 100, and 1000. Use left, right, and
midpoint rectangles, making a table of the answers, rounded to
three decimal places.
n
Left
Midpoint
Right
10
100
1000
(b) Find the exact value of the area under the curve by
evaluating an appropriate definite...

Let f(x) = x2, and compute
the Riemann sum of f over the interval [5, 7], choosing
the representative points to be the left endpoints of the
subintervals and using the following number of subintervals
(n). (Round your answers to two decimal places.)
(a) two subintervals of equal length (n = 2)
(b) five subintervals of equal length (n = 5)
(c) ten subintervals of equal length (n = 10)
(d) Can you guess at the area of the region...

6.3 2. Let f(x) = x2, and
compute the Riemann sum of f over the interval [8, 10],
choosing the representative points to be the midpoints of the
subintervals and using the following number of subintervals
(n). (Round your answers to two decimal places.)
a. two subintervals of equal length (n = 2)
___________
b. five subintervals of equal length (n = 5)
__________
c. ten subintervals of equal length (n = 10)
_________
d. Can you guess at the...

Use the Riemann Sum (limit process) to find the area between y =
x 2 + 2x and x-axis over the interval [0, 2].

Calculate the left Riemann sum for the given function over the
given interval, using the given value of n. (When
rounding, round your answer to four decimal places. If using the
tabular method, values of the function in the table should be
accurate to at least five decimal places.)
f(x) = 14 − 42x over [−1, 1], n = 4

Calculate the left Riemann sum for the given function over the
given interval, using the given value of n. (When
rounding, round your answer to four decimal places. If using the
tabular method, values of the function in the table should be
accurate to at least five decimal places.) HINT [See Example
2.]
f(x) = 26 −
78x over [−1, 1], n = 4

Calculate the left Riemann sum for the given function over the
given interval, using the given value of n. (When
rounding, round your answer to four decimal places. If using the
tabular method, values of the function in the table should be
accurate to at least five decimal places.) HINT [See Example
2.]
f(x) = e−x over [−3, 3], n = 3

Let f(x) = e^x. Evaluate a right Riemann sum for the interval
[−1, 1] for n = 4. You should include a picture of the
corresponding rectangles and state if this is an under or over
approximation of the area beneath the graph of f, above the x-axis
and between x = −1 and x = 1. In your solution, you should write
out all terms that go into the Riemann sum.

f(x) =
square root x
from a = 4 to b =
9
(a) Calculate the Riemann sum for the function for the following
values of n: 10, 100, and 1000. Use left, right, and
midpoint rectangles, making a table of the answers, rounded to
three decimal places.
n
Left
Midpoint
Right
10
100
1000
(b) Find the exact value of the area under the curve by
evaluating an appropriate definite integral using the Fundamental
Theorem. The values of the Riemann sums from...

A function f, a closed interval [a, b], and a number of equally
spaced subintervals n are given. Complete the following. f(x) = 7x;
[1, 4]; n = 6 (a) Calculate by hand the Left Sum to approximate the
area under the graph of f on [a, b]. (b) Calculate by hand the
Right Sum to approximate the area under the graph of f on [a,
b].
Here is a picture of the problem:
https://gyazo.com/e4d118fd3a49042c3b13a63a7d09ddf0

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