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: Vector Integration 2

  1. Mar 13, 2010 #1
    If A(t) = t i - t2 j + (t - 1) k and B(t) = 2t2 i + 6t k, evaluate (a) [tex]\int^{2}_{0}A \cdot B dt,[/tex] (b) [tex]\int^{2}_{0}A \times B dt.[/tex]
     
  2. jcsd
  3. Mar 14, 2010 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Doesn't sound too complicated, just plug in A and B, work out the vector products and do the integration using
    [tex]\int a t^n \, dt = \frac{a}{n + 1} t^{n + 1}[/tex]
     
  4. Mar 14, 2010 #3
    The solution I've made is not complicated.

    You try first to evaluate the vectors and then take the integral of them.
     
  5. Mar 14, 2010 #4

    HallsofIvy

    User Avatar
    Science Advisor

    What do you mean "the solution I've made"? You did not show any work or solution at all. What, exactly, are you asking?
     
  6. Mar 14, 2010 #5

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    I think he asks us to evaluate the integrals.
    I just did it.
     
  7. Mar 14, 2010 #6
    I evaluate the values of [tex]A\cdot B[/tex] and [tex]A\times B[/tex] first. Then integrate the both with respect to their limits.
     
  8. Mar 14, 2010 #7

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Yes, that is how you solve it.
    Halls meant: what exactly is your question (as in, problem, what you need our help with)?
     
  9. Mar 14, 2010 #8
    I didn't pretend that I know the answer.

    Here is my solution to the problem I posted.

    To letter (a). [tex]A\cdot B = 2t^{3} + 6t^{2} - 6t[/tex]

    Taking its integral with respect to t from 0 to 2 will give an answer of 12.

    To letter (b). [tex]A\times B = -6t^{3}i + [2t^{2} (t -1) - 6t^{2}]j - 2t^{4}k[/tex]

    Then, taking its integral with respect to t from 0 to 2 will result to [tex]-24 i- \frac{40}{3}j + \frac{64}{5} k[/tex]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook