   Chapter 5.5, Problem 56E ### 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

# Evaluate the definite integral. ∫ 0 3 d x 5 x + 1

To determine

To evaluate: The definite integral.

Explanation

Given:

The definite integral function is 03dx5x+1.

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

Calculation:

Consider u=5x+1 (1)

Differentiate both sides of the Equation (1).

du=5dxdx=15du

Calculate the lower limit value of u using Equation (1).

Substitute 0 for x in Equation (1).

u=5(0)+1=1

Calculate the upper limit value of u using Equation (1).

Substitute 1 for x in Equation (1).

u=5(3)+1=16

The definite integral function is,

03dx5x+1 (2)

Apply the lower and upper limit for u in Equation (2).

Substitute u for (5x+1) and (15du) for dx in Equation (2)

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