Using the three conditions, use the definition to evaluate the integral. Using the fact thatn(n+1)a. Σi-Li=12n(n+1)(2n+1)b. E-1i2 =Li=16n²(n+1)²c. Ei34Use the definitionп| f(x) dx = lim > f(a + iAx) Axn→∞ai=1to evaluate the following integral2х — 1 dx

Answered: Image /qna-images/answer/7dc02505-146d-4810-8c2e-e6c8c867f09d.jpg

Answered: Using the fact that n(n+1) a. E i = 2…

Using the fact that n(n+1) a. E i = 2 n(n+1)(2n+1) b. E-1i? = n?(n+1)? c. Li=1 E13 : 4 Use the definition п f (x) dx = lim > f (a + iAx) A» а i=1 to evaluate the following integral 4 2х — 1 dx

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Using the three conditions, use the definition to evaluate the integral.

Using the fact that
n(n+1)
a. Σi-
Li=1
2
n(n+1)(2n+1)
b. E-1i2 =
Li=1
6
n²(n+1)²
c. Ei3
4
Use the definition
п
| f(x) dx = lim > f(a + iAx) Ax
n→∞
a
i=1
to evaluate the following integral
2х — 1 dx

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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