1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find the definite integral of a vector

  1. Sep 13, 2012 #1
    1. The problem statement, all variables and given/known data

    If [itex]\vec{r}(t) = t^2\vec{i} + t\cos{(\pi t)}\vec{j} + \sin{(\pi t)}\vec{k}[/itex], evaluate [itex]\int_{0}^{1} \vec{r}(t) \text{dt}[/itex].

    2. Relevant equations

    3. The attempt at a solution

    So I tried integrating each individual part, and I got
    [itex]\frac{1}{3}t^3\vec{i} + (-\pi t\sin{(\pi t)} - \frac{\sin{(\pi t)}}{\pi})\vec{j} - \frac{\cos{(\pi t)}}{t}\vec{k} |_{0}^{1}[/itex]
    (For the coefficient of [itex]\vec{j}[/itex] I used integration by parts, I'm not sure if that's right because it looks weird)
    But evaluating at 0 makes the coefficient of [itex]\vec{k}[/itex] undefined! What should I do? Thanks.
  2. jcsd
  3. Sep 13, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You do realize that
    \int_{0}^{1} \vec{r}(t)\,dt=\hat{i}\int_{0}^{1} t^2\,dt+\hat{j}\int_{0}^{1} t\cos(\pi t)\,dt- \hat{k}\int_{0}^{1} \sin(\pi t)\,dt\ ,[/itex]​
    don't you?

    Show how you did the integration by parts, and show how you get a t in the denominator of the k component.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook