   Chapter 3.R, Problem 55E

Chapter
Section
Textbook Problem

# 55-58 Find f. f ′ ( t ) = 2 t − 3 sin t ,     f ( 0 ) = 5

To determine

To find:

The function f from the derivative function.

Solution:ft=t2+3cost+2

Explanation

1) Concept:

If F is an antiderivative of f on an interval I, then the most general antiderivative of f on I is Fx+c where c is an arbitrary constant.

Definition:

A function F  is called an antiderivative of f on an interval I if

F'x=fx f  For all x in I.

2) Formula:

Power rule of antiderivative

ddxxn+1n+1=xn

sinx=ddx-cosx

3) Given:

f't=2t-3sint,  f0=5

4) Calculations:

Here, f't=2t-3sint,  f0

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