Question

Use the Left and Right Riemann Sums with 100 rectangles to estimate the (signed) area under the curve of y=−2x+2 on the interval [0,50]. Write your answer using the sigma notation.

Answer #1

Given curve is y=-2x+2 on the interval [0,50]

Number of rectangles is 100, that is interval [0,50] is divided into 100 subintervals and length of each sub-interval is

Thus , the sub-intervals are

Thus area under given curve using left Riemann sums is

Area under given curve using Right Riemann sums is

Use the Left and Right Riemann Sums with 100 rectangles to
estimate the (signed) area under the curve of y=−10x+4y on the
interval [0,50]. Write your answer using the sigma notation.
Please show work, I'm very confused.

Use upper and lower sums (left and right Riemann sums) to
approximate the area
of the region below y =sqrt(8x) using 4 subintervals of each width.
Round to three
decimal places.

Estimate the area under the curve described by
f(x)=x2+1
between [1, 3] using 8 rectangles. You may define the height of
your rectangles using the left- or right-edge.

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...

Estimate the area of the region bounded between the curve f(x) =
1 x+1 and the horizontal axis over the interval [1, 5] using a
right Riemann sum. Use n = 4 rectangles first, then repeat using n
= 8 rectangles. The exact area under the curve over [1, 5] is ln(3)
≈ 1.0986. Which of your estimates is closer to the true value?

The rectangles in the graph below illustrate a left endpoint
approximation for the area under ?(?)=?^2/12 on the interval
[4,8].
The value of this left endpoint approximation is , and
this approximation is
an ? overestimate
of equal
to underestimate
of there is ambiguity the
area of the region enclosed by ?=?(?), the x-axis, and the vertical
lines x = 4 and x = 8.
Left endpoint approximation for area under ?=?212y=x212 on
[4,8][4,8]
The rectangles in the graph below illustrate a right endpoint
approximation for...

Estimate the area under the graph of f(x)=1/(x+3) over the
interval [−2,1] using ten approximating rectangles and
right endpoints. a=-2,b=1,n=10
Rn=?
Repeat the approximation using left endpoints.
Ln?
Accurate to 4 places.

Use a finite approximation to estimate the area under the graph
of the given function on the stated interval as instructed. 1) f(x)
= x 2 between x = 3 and x = 7 using a left sum with four rectangles
of equal width.

Estimate the area under the graph of
f(x)=1x+1f(x)=1x+1 over the interval [2,7][2,7] using eight
approximating rectangles and right endpoints.
Rn=Rn=
Repeat the approximation using left
endpoints.
Ln=Ln=
Round answers to 4
places. Remember not to round too early in your
calculations.

Estimate the area under the graph of f ( x ) = 1 x + 1 over the
interval [ 3 , 5 ] using two hundred approximating rectangles and
right endpoints
R n =
Repeat the approximation using left endpoints
L n =

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