   Chapter 5.5, Problem 73E ### 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 1 d x ( 1 + x ) 4

To determine

To evaluate: The definite integral.

Explanation

Given:

The definite integral function is 01dx(1+x)4.

The region lies between x=0 and x=1.

Calculation:

Take 1+x as u

u=1+xx=u1 (1)

Differentiate both sides of the Equation (1).

du=12xdxdx=2xdu (2)

Substitute (u1) for x in Equation (2).

2(u1)du=dx

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

Substitute 0 for t in Equation (1).

u=1+0=1

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

Substitute 1 for t in Equation (1).

u=1+1=2

The definite integral function is,

01dx(1+x)4 (3)

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

Substitute u for (1+x) and [2(u1)du] for dx in Equation (3).

01dx(1+x)4=121u4[2(u1)du]=212(uu41u4)du=212(1u31u4)du=212(u3u4)du (4)

Integrate Equation (4)

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