Chapter 8.1, Problem 64E

### 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

# Evaluating a Definite Integral In Exercises 57-72, evaluate the definite integral. Use a graphing utility to verify your result. ∫ − 3 1 e x e 2 x + 2 e x + 1   d x

To determine

To calculate: The definite integral and verify result by using the graphing utility.

Explanation

Given: âˆ«âˆ’31exe2x+2ex+1dx

Calculation:

Consider the integral,

âˆ«âˆ’31exe2x+2ex+1dx

Substitute,

u=exâˆ´du=exdx

Therefore,

âˆ«âˆ’31exe2x+2ex+1dx=âˆ«âˆ’311u2+2u+1du=âˆ«âˆ’311(u+1)2du=âˆ«âˆ’31(u+1)âˆ’2du

Apply the integration formula,

âˆ«undu=un+1n+1+c

Hence,

âˆ«âˆ’31exe

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Single Variable Calculus: Early Transcendentals, Volume I