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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A= y*z- w*(z-x)=10*5-5*(5-3)=50-5*2=50-10=40 in.^2
B is the answer
Answer:
truly ez points
Step-by-step explanation:
Answer:
x=2/3 y=-3
Step-by-step explanation:
2x+y=-3 *2 6x+2y=-6
3x+2y=-8
6x+2y-3x-2y=-6+8
3x=2
x=2/3
3*2/3+2y=-8
2+2y=-4
1+y=-2
y=-3