Question

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.

Answer #1

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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?

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 rectangles to estimate the area below the graph of y = f(x)
and over the x-axis on the interval [0,6]
Find left and right endpoints.

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
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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 area under the graph of f left parenthesis x right
parenthesis equals 5 x cubed f(x)=5x3 between x equals 0 x=0 and x
equals 1 x=1 using each finite approximation below. a. A lower sum
with two rectangles of equal width b. A lower sum with four
rectangles of equal width c. An upper sum with two rectangles of
equal width d. An upper sum with four rectangles of equal width

1) Use finite approximation to estimate the area under the graph
of f(x) = x^2 and above the graph of f(x) = 0 from Xo = 0 to Xn= 2
using
i) a lower sum with two rectangles of equal width
ii) a lower sum with four rectangles of equal width
iii) an upper sum with two rectangles of equal width
iv) an upper sum with four rectangles if equal width
2) Use finite approximation to estimate the area under...

Estimate the area under the graph of f(x)=1/(x+2) over the
interval [0,3]using eight approximating rectangles and
right endpoints.
Rn=
Repeat the approximation using left endpoints.
Ln=

f(x) = x^2+1
-Estimate area between graph f(x) & x-axis
-interval : [1,3]
- n=4 rectangles
- method: left-endpoint

1. Find the area of the region bounded by the graph of the
function f(x) = x4 − 2x2 + 8, the
x-axis, and the lines x = a and
x = b, where a < b and
a and b are the x-coordinates of the
relative maximum point and a relative minimum point of f,
respectively.
2.Evaluate the definite integral.
26
2
2x + 1
dx
0
3. Find the area of the region under the graph of f...

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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.
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