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kupik [55]
3 years ago
14

Branliest offered

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
8 0
1/9
2
1 4/5
3 1/2

There's your answer.
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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}) dxis 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}) dxis 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
2 years ago
A square pool has a side length of x feet.A uniform border around pool is 1 footwide.The total area of the pool and the border o
lions [1.4K]
The total area of pool and border = 361  square feet.

Length of square pool = x

Length of square pool plus border =  (x + 1 +1 ) = x + 2

There is 1 foot length on each side on the x  length.

The other length of the square pool and border =  (x + 2)

Area = (x+2)(x+2)

     (x + 2)(x +2) =  361.            Let A = x +2

        A*A = 361
            A²  = 361    Take square root of both sides
             A  = √361
               A = 19

A = x + 2 = 19
       x = 19 - 2
       x = 17

Area of square pool = x*x = 17*17 = 289

Area of the pool = 289 square feet.
8 0
3 years ago
How do i simplify this equation?
elixir [45]

Answer:

-6 = m (i'll show my work below)

Step-by-step explanation:

-6(m-7) + 7 = -8m + 37

-6m + 42 + 7 = -8m + 37

-6m + 49 = -8m +37

     -37     =      -37

-6m + 12  =  -8m

+6m       =    +6m

12 = -2m

/-2 = /-2

-6 = m

8 0
3 years ago
Which equation illustrates the commutative property of addition?
lbvjy [14]
<span>commutative property of addition
answer is

</span><span>A. 12 + 6 + 15 = 12 + 15 + 6</span>
3 0
3 years ago
Read 2 more answers
Eleana and her grandfather both had birthdays last week.
disa [49]

Answer:

25

Step-by-step explanation:

7 0
3 years ago
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