   Chapter 5, Problem 24RE ### 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 integral, if it exists. ∫ 0 1 e x 1 + e 2 x   d x

To determine

The value of the integral function.

Explanation

Given information:

The integral function is 01ex1+e2xdx

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

Calculation:

Express the function f(x) as shown below:

f(x)=ex1+e2x (1)

Divide numerator and denominator of the function by ex as shown below:

f(x)=exex1ex+e2xex=1ex+ex (2)

The expression to find the integral value as shown below:

01ex1+e2xdx=01(1ex+ex)dx=01sechx2dx=1201coshxsinh2x+1dx (3)

Consider sinhx as u.

u=sinhx (4)

Differentiate both sides of the Equation

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