Question

6.3 2. Let *f*(*x*) = *x*^{2}, 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 area of the region under the graph of
*f* on the interval [8, 10]?

_________square units

Answer #1

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...

Let f(x)=10-2x
a.) Sketch the region R under the graph of f on the interval
[0,5], and find its exact area using geometry.
b.) Use a Riemann sum with five subintervals of equal length
(n=5) to approximate the area of R. Choose the representative
points to be the left endpoints of the subintervals.
c.) Repeat part (b) with ten subintervals of equal length
(n=10).
d.) Compare the approximations obtained in parts (b) and (c)
with the exact area found in...

1. Evaluate the Riemann sum for
f(x) = 2x − 1, −6 ≤ x ≤ 4,
with five subintervals, taking the sample points to be right
endpoints.
2. sketch a graph
3. Explain.
The Riemann sum represents the net area of the rectangles with
respect to the .....

Evaluate the Riemann sum for f ( x ) = 0.4 x − 1.7 sin ( 2 x )
over the interval [ 0 , 2 ] using four subintervals, taking the
sample points to be midpoints. M 4 =
step by step solution is needed. answer to 6 decimal place.

Consider the region bounded by f(x) = x^3 + x + 3 and y = 0 over
[−1, 2].
a) Find the partition of the given interval into n subintervals
of equal length. (Write ∆x, x0, x1, x2, · · · , xk, · · · ,
xn.)
b) Find f(xk), and setup the Riemann sum ∑k=1 f(xk)∆x.
c) Simplify the Riemann sum using the Power Sum Formulas.
d) Find the area of the region by taking limit as n...

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.

A) Find an approximation of the area of the region R
under the graph of the function f on the interval [0, 2].
Use n = 5 subintervals. Choose the representative points
to be the midpoints of the subintervals.
f(x)=x^2+5
=_____ square units
B) Find an approximation of the area of the region R
under the graph of the function f on the interval [-1, 2].
Use n = 6 subintervals. Choose the representative points
to be the left endpoints...

Evaluate the Riemann sum for f ( x ) = ln ( x ) − 0.9 over the
interval [ 1 , 5 ] using eight subintervals, taking the sample
points to be right endpoints. R 8 = step by step and answer
please..

(a) Find the Riemann sum for
f(x) = 3
sin(x), 0 ≤ x ≤
3π/2,
with six terms, taking the sample points to be right endpoints.
(Round your answers to six decimal places.)
R6 =
(b) Repeat part (a) with midpoints as the sample points.
M6 =
Express the limit as a definite integral on the given
interval.
lim n → ∞
n
7xi* +
(xi*)2
Δx, [3, 8]
i = 1
8
dx
3

Let R denote the region that lies below the graph of y = f(x)
over the interval [a, b] on the x axis. Calculate an underestimate
and an overestimate for the area A of R, based on a division of [a,
b] into n subintervals all with the same length delta(x) = (b -
a)/n.
f(x) = 9 - x2 on [0, 3]; n = 5

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