Question

A function f, a closed interval [a, b], and a number of equally spaced subintervals n are given. Complete the following. f(x) = 7x; [1, 4]; n = 6 (a) Calculate by hand the Left Sum to approximate the area under the graph of f on [a, b]. (b) Calculate by hand the Right Sum to approximate the area under the graph of f on [a, b].

Here is a picture of the problem: https://gyazo.com/e4d118fd3a49042c3b13a63a7d09ddf0

Answer #1

A function f, a closed interval [a, b], and a number of equally
spaced subintervals n are given. Complete the following. f(x) = 6x;
[1, 4]; n = 6 (a) Calculate by hand the Left Sum to approximate the
area under the graph of f on [a, b]. Incorrect: Your answer is
incorrect. (b) Calculate by hand the Right Sum to approximate the
area under the graph of f on [a, b].
Here is a picture of the problem:
https://gyazo.com/e025257aff15effde694185276a2e24c

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...

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

Estimate the area under the curve f(x) = sin(x) from
using 6 subintervals and a right hand sum. Repeat this but use a
left hand sum
from x=0 to x= pi/2

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...

For the function given below, find a formula for the Riemann
sum obtained by dividing the interval [a,b] into n equal
subintervals and using the right-hand endpoint for each
c Subscript kck.
Then take a limit of this sum as
n right arrow infinityn → ∞
to calculate the area under the curve over [a,b].
f(x)equals=44x
over the interval
[00,44].
Find a formula for the Riemann sum.

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...

The average value of a positive function over an interval [a,b]
is given by the area underneath the graph of the function divided
by the length of the interval. Use a finite sum to estimate the
average value of ?(?)=1/? on the interval [1,25] by partitioning
the interval into four subintervals of equal length and evaluating
f at the midpoints of the subintervals. Estimate for average value
is

The average value of a positive function over an interval [a,b]
is given by the area underneath the graph of the function divided
by the length of the interval. Use a finite sum to estimate the
average value of ?(?)=1/? on the interval [1,25] by partitioning
the interval into four subintervals of equal length and evaluating
f at the midpoints of the subintervals. Estimate for average value
is

Approximate the area under the graph of the function y = x^3:
from [0,8] for n = 8 subintervals. Show all work for finding of
upper and lower sum(s).

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