Length of an Objects path in 3D Space

[WakelessFoil]

Need help for an exam tomorrow morning. Can someone help me check my work for this Calculus 3 problem? We are given a vector function for the acceleration of an object through space. We integrate to find velocity and then find the magnitude of the velocity vector and integrate the result with given bounds of t? Is the the correct approach to solving this?



Thanks!
Justin

 

[Cubist]

We are given a vector function for the acceleration of an object through space. We integrate to find velocity and then find the magnitude of the velocity vector and integrate the result with given bounds of t? Is the the correct approach to solving this?

The first of your three lines of work shows the velocity vector. This result is correct.

Your second line shows the answer to question "3a". This expression could be simplified.

Your third line shows how to calculate the answer to question "3b". The final answer is shown in a box to the right but I have no idea how you obtained that result (perhaps you could show your full working?). However, I get the same answer if I do the work myself


EDIT: Actually your first line is the answer to question "3a" since the question asks for velocity (not speed). Your second line shows the speed (the magnitude of the velocity vector). Hint: simplification of this line makes the answer to "3b" much easier!