Question

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 .....

Answer #1

Evaluate the Riemann sum for
f(x)=0.4x−1.8sin(2x)f(x)=0.4x-1.8sin(2x) over the interval
[0,2][0,2] using four subintervals, taking the sample points to be
right endpoints.
R4=
step by step with answer please

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..

5. A problem to connect the Riemann sum and the Fundamental
Theorem of Calculus:
(a) Evaluate the Riemann sum for f(x) = x 3 + 2 for 0 ≤ x ≤ 3
with five subintervals, taking the sample points to be right
endpoints.
(b) Use the formal definition of a definite integral with right
endpoints to calculate the value of the integral. Z 3 0 (x 3 + 2)
dx.
Note: This is the definition with limn→∞ Xn i=1 f(xi)∆x...

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.

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.

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...

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...

A particle is moving with the given data. Find the position of
the particle. a(t) = t2 − 5 t + 4, s'(0) = 0, s(1) = 1 s(t) =
Consider the function f(x) = x^2 - 2 x. Sketch the graph of f(x)
and divide the closed interval [-2,4] into 3 equal subintervals (To
get full credit, you must sketch the graph and corresponding
rectangles in your submitted work). a. Sketch the corresponding
rectangles by using Right endpoints in...

(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

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...

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