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Finding an integral using trig. substitution

  1. Sep 21, 2012 #1
    The integral from 0 to pi/2 of:

    cos(t)/sqrt(1+sin^2(t)) dt

    I'm supposed to use trig. substitution to find the solution. I started by using the formula a^2+x^2 to get x=atanx. In this case, sin(t)=(1)tan(θ), and so cos(t)dt=sec^2(θ)dθ and so I substituted this into the equation and got:

    sec^2(θ)/sqrt(1+tan^2(θ)) -> sec^2(θ)/sqrt(sec^2(θ)) -> sec(θ)

    Now, I have the integral of sec(θ)dθ, which equals ln abs(secθ+tanθ). When I take this integral at 0, it turns out to be 0, and so I'm left with the answer being solely the integral at pi/2. The problem is that the secant at pi/2 is infinity and so is the tangent at pi/2, and so the answer ends up being infinity, and this is apparently wrong.

    Any help would be greatly appreciated.
     
  2. jcsd
  3. Sep 21, 2012 #2
    It would be better if you substitute sin(t)=x.
     
  4. Sep 21, 2012 #3

    Mark44

    Staff: Mentor

    A trig substitution can be used after you use the substitution that Pranav-Arora recommends.
     
  5. Sep 21, 2012 #4
    I substituted sin(t)=x and got:

    1/sqrt(1+x^2)dx

    but when I use the trig. substitution with this integral, I come up with the same thing I had before. I don't think I understand how to do it substituting sin(t)=x and then using a trig. substitution, like Mark said.
     
  6. Sep 21, 2012 #5
    Never mind. I eventually figured out how to translate the upper and lower limits of the integrand over to the final versions. Thanks.
     
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