   Chapter 12.2, Problem 55E

Chapter
Section
Textbook Problem

# Evaluating a Definite Integral In Exercises 47-52, evaluate the definite integral. ∫ 0 2 ( t i + e t j − t e t k ) d t

To determine

To calculate: The simplified value of the definite integral 02(ti+etjtetk)dt.

Explanation

Given:

The definite integral 02(ti+etjtetk)dt.

Formula used:

If r(t)=f(t)i+g(t)j+h(t)k, where f, g, and h are continuous function on [a,b], then the definite integral of r is:

abr(t)dt=[abf(t)dt]i+[abg(t)dt]j+[abh(t)dt]k

Calculation:

Consider the following definite integral:

02(ti+etjtetk)dt

Evaluate the integration and substitute the limits of integration.

Thus, obtain the following result:

02(ti+etjtetk)dt=[02tdt]i+[02etdt]j[02tetdt]k

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