   Chapter 12.2, Problem 58E

Chapter
Section
Textbook Problem

# Finding an Antiderivative In Exercises 53-58, find r(t) that satisfies the initial condition(s). r ' ( t ) = 3 t 2 j + 6 t k ,     r ( 0 ) = i + 2 j

To determine

To calculate: The function r(t) where r(t)=3t2j+6tk satisfying the initial condition r(0)=i+2j.

Explanation

Given:

The derivative of vector valued function is r(t)=3t2j+6tk.

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

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)=3t2j+6tk

Evaluate the integration of the function as follows:

r(t)=r(t)dt=(3t2dt)j+(6tdt

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