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)=
⇒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=
∑
=4
∑
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:
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
x² - 12x + 11 = 0 ( subtract 11 from both sides )
x² - 12x = - 11
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 6)x + 36 = - 11 + 36
(x - 6)² = 25 ( take square root of both sides )
x - 6 = ±
= ± 5 ( add 6 to both sides )
x = 6 ± 5
Then
x = 6 - 5 = 1 ⇒ (1, 0 )
x = 6 + 5 = 11 ⇒ (11, 0 )
Answer:
100°
Step-by-step explanation:
The sum of the angles in a triangle is 180°
180°-30°-50°=100°
Answer:
f(-1) = 4
Step-by-step explanation:
See below for the synthetic division tableau. The remainder is 4, hence ...
f(-1) = 4
___
IMO, in this function it is far easier just to substitute -1 for x. Since the only terms are of even degree, the value of f(-1) is the sum of the coefficients:
f(-1) = -1 +1 +4
f(-1) = 4