# Average Valuesa. Verify that ?ln x dx = x ln x - x + C.b.

## Problem 117PE Chapter 5

Thomas' Calculus: Early Transcendentals | 13th Edition

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Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 117PE

Average Values

a. Verify that ∫ln x dx = x ln x - x + C.

b. Find the average value of ln x over [1, e].

Step-by-Step Solution:

Step 1:

In this question, we have to verify the given indefinite integral and find the average value of  over .

Step 2:

(a) The given indefinite integral is .

. Now integrating by parts taking  as the first function,

The integral is verified.

Step 3 of 3

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Average Valuesa. Verify that ?ln x dx = x ln x - x + C.b.

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