   Chapter 3.9, Problem 19E

Chapter
Section
Textbook Problem

# Find the most general antiderivative of the function. (Check your answer by differentiation.) f ( t ) = 8 t − sec t   tan t

To determine

To find:

The most general antiderivative of the given function.

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 for all x in I.

2) Formula:

The particular antiderivative of secxtanx is secx

Power rule of antiderivative

ddx xn+1n+1=xn

3) Given:

ft=8 t-sect tant

4) Calculation:

The given function is ft=8 t-sect tant

The particular antiderivative of secxtanx is secx

Using the particular antiderivatives,

The antiderivative of the function

ft=8 t-sect tant can be written as,

8 t12+112+1-secttant+C

8 t3232-sect+C

8·132  t32 -sect+C

8·23 t32 -sect+C

Which simplifies to,

F(t)=163<

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