Chapter 8.1, Problem 104E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# PUTNAM EXAM CHALLENGEEvaluate ∫ 2 4 ln ( 9 − x ) d x ln ( 9 − x ) + ln ( x + 3 ) . This problem was composed by the Committee on the Putnam Prize Competition.© The Mathematical Association of America. All rights reserved.

To determine

To calculate: The value of the integral, 24ln(9x)dxln(9x)+ln(x+3).

Explanation

Given:

The definite integral âˆ«24ln(9âˆ’x)dxln(9âˆ’x)+ln(x+3).

Formula used:

Definite Integral Property, âˆ«abf(x)dx=âˆ«abf(a+bâˆ’x)dx.

Calculation:

Consider the following definite integral:

âˆ«24ln(9âˆ’x)dxln(9âˆ’x)+ln(x+3)

Follow these steps to calculate the definite integral as follows:

Let, I=âˆ«24ln(9âˆ’x)dxln(9âˆ’x)+ln(x+3) â€¦â€¦ (1)

Use âˆ«abf(x)dx=âˆ«abf(a+bâˆ’x)dx the definite integral (1) can be reduced as shown below:

I=âˆ«24ln(9âˆ’(6âˆ’x))ln(9

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