Question

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 - x^{2} on [0, 3]; n = 5

Answer #1

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...

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...

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...

Let R be the region bounded above by f(x) = 3 times the (sqr
root of x) and the x-axis between x = 4 and x = 16. Approximate the
area of R using a midpoint Riemann sum with n = 6 subintervals.
Sketch a graph of R and illustrate how you are approximating it’
area with rectangles. Round your answer to three decimal
places.

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 of the subintervals.
f(x) = 5 − x2
_____ square units
2.
Find the area (in square units) of the region under the graph of
the function f on the interval
[5, 6].
f(x) = 8ex − x
____square units
Please answer both questions...

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.

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 R be the region bounded by y = x2 + 1, y = 0, x =
1, and x = 2. Graph the region R. Find the
volume of the solid generated when R is revolved
about the y-axis using (a) the Washer Method and
(b) the Shell Method.

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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