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Integration problem (need help)

  1. Jul 24, 2009 #1
    if a spaceship accelerates, from restat time t = 0, at a rate of 2t / sqrt(1 + t^2) m/s at time t, calculate in years to 1 significant figure how long it would take to reach the speed of light?

    my attempt

    speed of light = 3.0 x 10^8 m/s
    integrate the rate function 2t / sqrt(1 + t^2) from t = 0, to the t we are looking for

    integrating 2t / sqrt(1 + t^2)

    using integration by parts;

    let u = 1 + t^2, then du = 2t dt

  2. jcsd
  3. Jul 24, 2009 #2


    Staff: Mentor

    Before you go at an integral using integration by parts, you should always see if a simpler substitution will work. What you have shown is exactly the substitution I would use (your work does not show that you are doing integration by parts).

    Using this substitution, what does your new integral look like?
  4. Jul 24, 2009 #3


    User Avatar
    Science Advisor

    That is NOT "integration by parts". Perhaps you should review that.
    You want to integrate
    [tex]\int \frac{2t dt}{\sqrt{1+ t^2}}[/tex]
    and you say [itex]u= 1+ t^2[/itex] and [itex]du= 2tdt[/itex]. Okay, doesn't it make sense to replace the "2tdt" in the integral by du and the "[itex]1+ t^2[/itex] in the integral by u?
    You might want to remember that [itex]1/\sqrt{a}= a^{-1/2}[/itex].
  5. Jul 24, 2009 #4
    cheers, my mistake
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