   Chapter 12.2, Problem 56E

Chapter
Section
Textbook Problem

# Evaluating a Definite Integral In Exercises 47-52, evaluate the definite integral. ∫ 0 3 ‖ t i + t 2 j ‖   d t

To determine

To calculate: The simplified value of the definite integral 03ti+t2jdt.

Explanation

Given:

The definite integral is 03ti+t2jdt.

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 absolute value of r(t) is:

r(t)=f2+g2+h2

Calculation:

Consider the following definite integral:

03ti+t2jdt

Evaluate the integration and substitute the limits.

Thus, obtain the following result:

03ti+t2jdt=03[(t)2+(t2)2]dt=03(t1+t2)dt

Substitute 1+t2=u.

Thus,

2tdt=dutdt=12du

At t=0, u=1

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 1-6, simplify the expression. 11(1x)

Calculus: An Applied Approach (MindTap Course List)

#### Expand each expression in Exercises 122. (3x+1)(2x2x+1)

Finite Mathematics and Applied Calculus (MindTap Course List)

#### A sample of n = 9 scores has X = 108. What is the sample mean?

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### 10003/2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 27-30, find. 28.

Mathematical Applications for the Management, Life, and Social Sciences

#### Multiply: (3)(9)

Elementary Technical Mathematics

#### n=12(14)n converges to: a) 94 b) 2 c) 23 d) the series diverges

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

#### Define content analysis and archival research.

Research Methods for the Behavioral Sciences (MindTap Course List) 