Question

Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0, 1] for lim n-> infinity sigma i=1 7i^3/2n^4

Answer 1

OKay Nvm I figured it out.
Rewrite this as
lim(n→∞) Σ(i = 1 to n) (7/2)(i/n)^3 * (1/n)
= ∫(0 to 1) (7/2)x^3 dx, with Δx = 1/n and f(x) = (7/2)x^3
(i/n) since (a+(b-a)i/n)
= (7/8)x^4 {for x = 0 to 1} USE ANTI-Derivative
= 7/8.

Answer 2

\[\int_0^1 \frac{7 x^3}{2} \, dx=\frac 7 8
\]