   Chapter 12.2, Problem 60E

Chapter
Section
Textbook Problem

# Finding an Antiderivative In Exercises 53-58, find r( t) that satisfies the initial condition(s). r " ( t ) = − 4 cos t j − 3 sin t k , r ' ( 0 ) = 3 k , r(0)=4 j

To determine

To calculate: The function r(t) that satisfy the initial conditions r'(0)=3k, r(0)=4j for r''(t)=4costj3sintk.

Explanation

Given:

The provided function is r''(t)=4costj3sintk and the provided initial conditions are r'(0)=3k, r(0)=4j.

Formula used:

The formula of integration of the function sinx and cosx is:

cosxdx=sinxsinxdx=cosx

Calculation:

Consider theprovided function r''(t)=4costj3sintk.

ddt[r'(t)]=4costj3sintk

Integrate the above expression by help of integration formula of sint,costcosdt=sint and sintdt=cost

r'(t)=4sintj+3costk+c …… (1)

It could be write as,

ddt [r(t)]=4sintdtj+3costdtk+cdt

Now, Integrate the above expression to get;

d[r(t)<

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