   Chapter 12.2, Problem 61E

Chapter
Section
Textbook Problem

# Finding an Antiderivative In Exercises 53-58, find r(t) that satisfies the initial condition(s). r ' ( t ) = t e − t 2 i − e − t j + k ,     r ( 0 ) = 1 2 i − j + k

To determine

To calculate: The value of r(t) that satisfies the initial condition(s) of r'(t)=tet2ietj+k and r(0)=12ij+k.

Explanation

Given:

The initial condition is r'(t)=tet2ietj+k and r(0)=12ij+k.

Calculation:

It is provided that r'(t)=tet2ietj+k so, it can also be written as:

ddtr(t)=tet2ietj+kdr(t)=(tet2ietj+k)dt

Integrate both sides as:

dr(t)=(tet2ietj+k)dtr(t)=12et2i+etj+tk+c

Now, it is also given that r(0)=12ij+k

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