Average Velocity of a particle

[lude1]

Homework Statement

The velocity, in ft/sec, of a particle moving along the x-axis is given by the function v(t) = e^t + te^t. What is the average velocity of the particle from time t=0 to time t=3?

Answer: 20.086

Homework Equations

The Attempt at a Solution

Average velocity means the derivative formula, [s(t + Δt) - s(t)] / (Δt)
In other words, I get

[v(3) - v(0)] / (3-0)
[e³ - 3e³] / 3
And I got 26.447​

However, the answer is 20.086.

What did I do wrong?

 

[Mark44]

Homework Statement

The velocity, in ft/sec, of a particle moving along the x-axis is given by the function v(t) = e^t + te^t. What is the average velocity of the particle from time t=0 to time t=3?

Answer: 20.086

Homework Equations

The Attempt at a Solution

Average velocity means the derivative formula, [s(t + Δt) - s(t)] / (Δt)
In other words, I get

[v(3) - v(0)] / (3-0)
[e³ - 3e³] / 3
And I got 26.447​

However, the answer is 20.086.

What did I do wrong?

The average value of a function f(x) on an interval [a, b] is
$$\frac{1}{b - a} \int_a^b f(x) dx$$