How to do this Calculus AB question?

Test Preparation AP Test Preparation
1

<p>I thought it was easy but apparently I got it wrong -_-</p>

<p>"A particle travels along a straight line with a velocity of v(t) = 3e^(-t/2) * sin(2t) meters per second. What is the total distance in meters traveled by the particle during the time interval 0 <= t <= 2"</p>

<p>A. 0.835
B. 1.850
C. 2.055
D. 2.261
E. 7.025</p>

<p>I thought you could just integrate it over the interval 0 to 2. What am I doing wrong?</p>

<p>Thanks</p>

2

<p>Explained accurately below. Total distance, not positive distance. That is what I get for taking AP Spanish today and being drained.</p>

3

<p>You have to integrate the absolute value of the velocity function. Total distance is the integral of the absolute value of the velocity. Total displacement is the integral of the velocity. So the answer is D.</p>

4

<p>Ah, ok that makes sense. The Calculus test seems to have a lot of tricky questions >.></p>

5

<p>byubound speaks the truth.</p>

<p>edit - for some questions, make note of the initial position. Position will be integral of function + initial position.</p>

6

<p><a href=“integrate from 0 to 2 (abs(3e^(-t/2) * sin(2t))) - Wolfram|Alpha”>integrate from 0 to 2 (abs(3e^(-t/2) * sin(2t))) - Wolfram|Alpha;

7

<p>^Nice. Basically fnInt( on steroids. :)</p>