AP Calc Free Answer Problem:Change Over Time

[chrisdude112]

Homework Statement

A Particle Moves along the x-axis so that its velocity v at time t \geq 0 is given by v(t)=Sin(x^{2}). The Graph of V is shown above for 0 \geq t \geq \sqrt{5\pi}. The Position of the particle at time t is x(t) and its position at time t=0 is x(0)=5

Homework Equations

Find the total Distance traveled b the particle from time t=0 to t=3.

The Attempt at a Solution

Homework Statement

We just started on integration so i figured we would need find the displacement equation by integrating the velocity equation, which would be finding:
\int Sin(x^{2} dt [0,3]. From here i have no idea how to do the equation since we're only 2 weeks into integration and have barely touched \mu Substitution

 

[rock.freak667]

The only way I can see to do it is to take the taylor series of sinx and replace all the x's by x^2 and then approximate the terms.

 

[chrisdude112]

oh thanks, in your opinion do you think that this problem is quite difficult for an AB AP Calculus Class?

 

[jambaugh]

If the graph of the velocity is given, can you use this alone to find the distance? Remember the original definition of the integral of a function!

[also remember that as in real life, not all information available to you need be relevant.]

 

[chrisdude112]

If the graph of the velocity is given, can you use this alone to find the distance? Remember the original definition of the integral of a function!

[also remember that as in real life, not all information available to you need be relevant.]

Oh. Are you referring to a of a Rieman's Sum approach to solving the equation by means of RRAM/MRAM/LRAM, Simpsons, Trapezoidal rule?