   Chapter 12.2, Problem 57E

Chapter
Section
Textbook Problem

# Finding an Antiderivative In Exercises 53-58, find r( t) that satisfies the initial condition(s). r ' ( t ) = 4 e 2 t i + 3 e t j , r ( 0 ) = 2 i

To determine

To calculate: The function r(t), where r(t)=4e2ti+3etj satisfying the initial condition r(0)=2i.

Explanation

Given:

The derivative of vector valued function is r(t)=4e2ti+3etj.

And the initial condition is r(0)=2i.

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 derivative:

r(t)=4e2ti+3etj

Evaluate the integration of the function as follows:

r(t)=r(t)dt=(4e2tdt)i+(3et<

### 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

#### Find more solutions based on key concepts 