HELP ME PLEASEEE 20 POINTSSS!!!!

Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your

Veronika [31]

The expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Given an integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ .

We are required to express the integral as a limit of Riemann sums.

An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.

A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.

Using Riemann sums, we have :

$\int\limits^b_a {f(x)} \, dx$ = $\lim_{n \to \infty}$ ∑f(a+iΔx)Δx ,here Δx=(b-a)/n

$\int\limits^5_1 {x/(2+x^{3}) } \, dx$ =f(x)= $x/2+x^{3}$

⇒Δx=(5-1)/n=4/n

f(a+iΔx)=f(1+4i/n)

f(1+4i/n)= $[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}$

$\lim_{n \to \infty}$ ∑f(a+iΔx)Δx=

$\lim_{n \to \infty}$ ∑ $n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n$

=4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$

Hence the expression of integral as a limit of Riemann sums of given integral $\int\limits^5_b {1} \, x/(2+x^{3}) dx$ is 4 $\lim_{n \to \infty}$ ∑ $n(n+4i)/2n^{3}+(n+4i)^{3}$ from i=1 to i=n.

Learn more about integral at brainly.com/question/27419605

#SPJ4

5 0

1 year ago

Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state thi

vladimir2022 [97]

The answer is x = 10, y = 10.

Step 1: rearrange the second equation for y.
Step 2: substitute y from the second equation into the first equation.
Step 3. Calculate y.

Step 1.
The second equation is: 6x + 3y = 90
Divide both sides of the equation by 3:
(6x + 3y)/3 = 90/3
6x/3 + 3y/3 = 30
2x + y = 30
Rearrange the equation:
y = 30 - 2x

Step 2.
Substitute y from the second equation (y = 30 - 2x) into the first equation:
15x + 9y = 240
15x + 9(30 - 2x) = 240
15x + 270 - 18x = 240
15x - 18x = 240 - 270
-3x = -30
x = -30/-3
x = 10

Step 3.
Since y = 30 - 2x and x = 10, then:
y = 30 - 2 * 10
y = 30 - 20
y = 10

6 0

2 years ago

PLEASE HELP FAST answers: a.) 4 b.) 10 c.) 6 d.) 1

VLD [36.1K]

Answer:

4

Step-by-step explanation:

There are 5 points. So there are 4 segments. The segments are the line between two points.

6 0

3 years ago

Can someone help me?

choli [55]

Answer:

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Does the construction demonstrate how to bisect a segment correctly by hand?

Aleonysh [2.5K]

Answer:

Yes; the compass was kept at the same width to create the arcs for points C and D.

Step-by-step explanation:

When bisecting a segment by hand the steps are:

-Place the compass on one of the endpoints and open the compass to a distance more than halfway across the segment.

-Swing an arc on either side of the segment.

-Keeping the compass at the same width, place the compass on the other endpoint and swing arcs on either side so that they intersect the first two arcs created.

-Mark the intersection points of the arcs and draw a line through those two points.

-The point where this new line crosses the given segment is the midpoint and divides the segment in half.

Its not b because segment c and d was created when you marked the intersection points of the arcs and just drew a line through those two points; They didn't use a straightedge. its not C because this does demonstrate how to bisect a segment by hand, Also the compass was kept at the same width to create the arcs for points C and D. Its not D because this does demonstrate how to bisect a segment by hand, Also a straightedge was not used to create segment CD.

6 0

2 years ago

Read 2 more answers