   Chapter 5.2, Problem 60E ### 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

# Use Property 8 to estimate the value of the integral. ∫ 0 3 1 x + 4 d x

To determine

To calculate: The value of the integral function 031x+4dx.

Explanation

Given information:

The integral function is 031x+4dx (1)

Consider the function f(x)=1x+4 (2)

The region lies between x=0 and x=3.

Apply Property 8 of integrals:

If mf(x)M for axb, then m(ba)abf(x)dxM(ba).

To find the absolute maximum value M as shown below:

Calculate absolute maximum value using Equation (2).

M=f(x) (3)

Substitute 0 for x in Equation (3).

M=f(0)=10+4=14

To find the absolute minimum value m as shown below:

Calculate minimum value using Equation (1)

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 