Question

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 of the subintervals.

f(x)=4-x^2

=_____ square units

Find an approximation of the area of the region *R* under
the graph of the function *f* on the interval [1, 3]. Use
*n* = 4 subintervals. Choose the representative points to be
the right endpoints of the subintervals.

f(x)=7/x

=_____ square units.

Answer #1

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...

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...

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...

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 =

Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with n=4.
f(x)=e^x+1 fromx=-2 to x=2
(a) Use left endpoints.
(b) Use the right endpoints.
(c) Average the answers in parts (a) and (b)
(d) Use midpoints.
The area, approximated using the left endpoints, is
The area, approximated using the right endpoints, is
The average of the answers in parts (a) and (b) is
The area, approximated using the midpoints, is

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...

Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with n=4
f(x)=e^x+5 from x=-2 to x=2
(a) Use left endpoints.
(b) Use right endpoints.
(c) Average the answers in parts (a) and (b)
(d) Use midpoints.

Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with n=4.
f(x)=6x+4 from x=3 to x=5
a) use left endpoints
b)use right endpoints
c) average the answers in parts a and b
d) use midpoints

approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with n=4.
f(x)=4x+5 from x=4 to x=6
A) use left endpoints
B) use right endpoints
C) average the answers in parts a and b
D) use midpoints

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...

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