The expression of integral as a limit of Riemann sums of given integral
is 4
∑
from i=1 to i=n.
Given an integral
.
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 :
=
∑f(a+iΔx)Δx ,here Δx=(b-a)/n
=f(x)=![x/2+x^{3}](https://tex.z-dn.net/?f=x%2F2%2Bx%5E%7B3%7D)
⇒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}](https://tex.z-dn.net/?f=%5Bn%5E%7B2%7D%28n%2B4i%29%5D%2F2n%5E%7B3%7D%2B%28n%2B4i%29%5E%7B3%7D)
∑f(a+iΔx)Δx=
∑![n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n](https://tex.z-dn.net/?f=n%5E%7B2%7D%28n%2B4i%29%2F2n%5E%7B3%7D%2B%28n%2B4i%29%5E%7B3%7D4%2Fn)
=4
∑![n(n+4i)/2n^{3}+(n+4i)^{3}](https://tex.z-dn.net/?f=n%28n%2B4i%29%2F2n%5E%7B3%7D%2B%28n%2B4i%29%5E%7B3%7D)
Hence the expression of integral as a limit of Riemann sums of given integral
is 4
∑
from i=1 to i=n.
Learn more about integral at brainly.com/question/27419605
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Answer:
3m^4
Step-by-step explanation:
the third one
Histogram
A histogram is a graphic display of quantitative variables that uses bars to represent the frequency of the count of the data in each interval. A boxplot is a graphic display of quantitative data that demonstrates the five-number summary.
As, synthetic division by -4 gives remainder 0. Hence, Option B is correct. -4 is a root of ![3x^{2} +7x-20](https://tex.z-dn.net/?f=%203x%5E%7B2%7D%20%2B7x-20%20)
As, x+4=0 gives x=-4.
So, option C is correct,
(x+4) is factor of ![3x^{2} +7x-20](https://tex.z-dn.net/?f=%203x%5E%7B2%7D%20%2B7x-20%20)
Option E is correct
![\frac{3x^{2} +7x-20 }{x+4}=3x-5](https://tex.z-dn.net/?f=%20%5Cfrac%7B3x%5E%7B2%7D%20%2B7x-20%20%7D%7Bx%2B4%7D%3D3x-5%20)