Question

Consider the functionf(x)=1−2x+x2. Estimate the area between f(x) and the x-axis over the interval 0≤x≤1 by setting up a Riemann summation with four equally spaced intervals and evaluating the function at the right hand side of each interval. Compare your answer with the exact answer.

Answer #1

For the function f(x) = x, estimate the area of the region
between the graph and the horizontal axis over the interval 0≤x≤4
using a .
a. Riemann Left Sum with eight left rectangles.
b. Riemann Right Sum with eight right rectangles.
c. A good estimate of the area.

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?

unctions, each over the interval x = 0 to x = 6:
f(x) = x2 + 1
f(x) = 12 − 2x
f(x) = 36 − x2
f(x) = 2x + 1
Methods:
R: Right Riemann sum
Number of Rectangles: 1,
Create a report on the application you selected. Include the
problem statement (function, interval, method, number of
rectangles), mathematical and verbal work of finding the
approximate area under the curve, a graph of the
function/rectangles created at the Desmos...

Consider the function f(x)=4x2-x3 provide
the graph the region bounded by f(x) and the x-axis over the
interval [0,4], then estimate the area of this region using left
reman sum with n=4, 10 and 20 subintervals. you may use the
graphing calculator to facilitate the calculation of the Riemann
sum. use four decimal places in all your calculations and
answers.

Use finite approximations to estimate the area under the graph
of the function f(x) =8−x2+2x between x = −2 and x = 4 for each of
the following cases. a. Using a lower sum with two rectangles of
equal width b. Using a lower sum with four rectangles of equal
width c. Using an upper sum with two rectangles of equal width d.
Using an upper sum with four rectangles of equal width

Estimate the instantaneous rate of change of the function
f(x)=−x2+2x+1 at x=2 using the average rate of change over
successively smaller intervals.

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

Approximate the area under the curve over the specified interval
by using the indicated number of subintervals (or rectangles) and
evaluating the function at the right-hand endpoints of the
subintervals.
f(x) = 25 − x2 from x = 1 to x = 3; 4
subintervals

Consider the function f(x)=1/x on the interval [1,2]. Let P be a
uniform partition of [1,2] with 8 sub-intervals. Compute the left
and right Riemann sum of ff on the partition. Enter approximate
values, rounded to three decimal places.

Use finite approximations to estimate the area under the graph
of the function f(x) = 24−x2+2x between x = −4 and x = 6 for each
of the following cases. a. Using a lower sum with two rectangles of
equal width b. Using a lower sum with four rectangles of equal
width c. Using an upper sum with two rectangles of equal width d.
Using an upper sum with four rectangles of equal width

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