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## Homework Statement

An object moves with velocity v(t) = −t

^{2}+1 feet per second between t = 0 and t = 2. Find the average velocity and the average speed of the object between t = 0 and t = 2

## Homework Equations

[itex]

\frac{1}{b-a} \int_a^b f'(x) dx

[/itex]

avg value of a function

## The Attempt at a Solution

[itex]

\frac{1}{2-0} \int_0^2 [-t^2 + 1] dt

[/itex]

[itex]

\frac{1}{2} [- \frac{t^3}{3} + t]_0^2

[/itex]

[itex]

\frac{1}{2} [- \frac{8}{3} + \frac{6}{3}]

[/itex]

[itex]

\frac{1}{2} [- \frac{2}{3}]

[/itex]

[itex]

[- \frac{1}{3}]

[/itex]

So I've got the average velocity down, but I don't see how they want me to come up with the average speed. I know that speed and velocity are similar, but speed has no direction.

The book (http://www.whitman.edu/mathematics/multivariable/" [Broken]) Instructed me to evaluate the integral without the averaging [itex]\frac{1}{b-a}[/itex], but I ended up with:

[itex]

- \frac{2}{3}

[/itex]

But according to the solutions manual, the answer is 1

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