   Chapter 4.3, Problem 12E

Chapter
Section
Textbook Problem

Writing a Limit as a Definite Integral In Exercises 11 and 12, write the limit as a definite integral on the given interval, where c i is any point in the ith subinterval. Limit Interval lim ‖ Δ ‖ → 0 ∑ i = 1 n c i 2 + 4 Δ x i , [ 0 , 3 ]

To determine

To calculate: Limit limΔ0i=1n(ci2+4)Δxi as a definite integral on interval [0,3].

Explanation

Given: limΔ0i=1n(ci2+4)Δxi in the interval [0,3]

Formula used:

Formula for the definite integral of f(x) from a to b is defined as:

abf(x)dx=limΔ0i=1nf(ci)Δxi

where, a is the lower limit of integration and b is the upper limit of integration.

Calculation:

Formula for definite integral is:

abf(x)dx=limΔ0i=1nf(ci)Δxi …… (1)

Given limit:

abf(x)dx=limΔ0i=1n(ci2+4)Δxi …… (2)

Compare equation (1) and equation (2)

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