Question

Approximate the area under the curve on the specified interval as directed. f(x) = x · 10^x on [0, 4] with 4 subintervals of equal width and midpoints for sample points?

Answer #1

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

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...

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...

Question 4.
f(t)=2t^3+2
What is the approximate area under the graph of f(t) on
the interval [0, 6] using two rectangles of equal
width and left endpoints?

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...

F(x)=4x-x^2
x= 0 to 2
two sub intervals
Approximate the area under the curve over the interval.

Approximate the area under the curve y = 12x−4x2 between x = 0
and x = 2 using four rectangles of the same width and the
right-hand endpoint method.

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

1. 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) = −x2 + 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.
2. 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)...

Sketch the area under the standard normal curve over the
indicated interval and find the specified area. (Round your answer
to four decimal places.) The area to the right of z = −1.13 is
.
Sketch the area under the standard normal curve over the
indicated interval and find the specified area. (Round your answer
to four decimal places.) The area to the right of z = −2.15 is
.
Sketch the area under the standard normal curve over the...

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