Chapter 5.3, Problem 11E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Writing a Limit as a Definite Integral In Exercises 11-14, write the limit as a definite integral on the given interval, where c i is any point in the ith subinterval. lim ‖ Δ ‖ → 0 ∑ i = 1 n ( 3 c i + 10 ) Δ x i ,   [ − 1 ,   5 ]

To determine

To calculate: The limit limΔ0i=1n(3ci+10)Δxi as a definite integral on the provided interval [1,5]

Explanation

Given:

The provided limit is limâ€–Î”â€–â†’0âˆ‘i=1n(3ci+10)Î”xi in the interval [âˆ’1,5].

Formula used:

The definite integral of f(x) from a to b is defined as:

âˆ«abf(x)dx=limâ€–Î”â€–â†’0âˆ‘i=1nf(ci)Î”xi

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

Calculation:

The formula for definite integral is:

âˆ«abf(x)dx=limâ€–Î”â€–â†’0âˆ‘i=1nf(ci)Î”xi â€¦â€¦ (1)

The provided limit is:

âˆ«abf(x)dx=limâ€–Î”â€–â†’0âˆ‘i=1n(3ci+10)Î”xi â€¦â€¦ (2)

Compare equation (1) and equation (2)

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