   Chapter 5.2, Problem 19E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Express the limit as a definite integral on the given interval. lim n → ∞ ∑ i = 1 n [ 5 ( x i * ) 3 − 4 x i * ]   Δ x ,   [ 2 , 7 ]

To determine

To express: The limits of the function limni=1n[5(xi)34xi]Δx as a definite integral with the given interval.

Explanation

Given information:

The limitsof the function is limni=1n[5(xi)34xi]Δx

The function lies with the interval [2,7].

Calculation:

The expression of Theorem 4 is shown below:

abf(x)dx=limni=1nf(xi)Δx (1)

Here, the upper limit is b and the lower limit is a.

Substitute xi for xi in Equation (1).

abf(x)dx=limni=1nf(xi)Δx (2)

Compare the function limni=1n[5(xi)34xi]Δx with Equation (2).

f(xi)=(5(xi)34xi) (3)

Substitute x for xi in Equation (3)

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