Results 1 to 2 of 2

Math Help - [SOLVED] Verify trig substitution

  1. #1
    Senior Member mollymcf2009's Avatar
    Joined
    Jan 2009
    From
    Charleston, SC
    Posts
    490
    Awards
    1

    [SOLVED] Verify trig substitution

    Hey y'all!

    Here is my integral:

    75 \int sec^2x tanx dx

    The book does the substitution with u = tanx, du = sec^2x dx

    I worked mine out before I looked at the answer, I changed everything to terms of sin and cos and worked it that way.

    My answer:

    \frac{75}{2cos^2x} + C

    Book answer:

    \frac{75}{2} tan^2x + C

    Is my answer wrong?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    o_O
    o_O is offline
    Primero Espada
    o_O's Avatar
    Joined
    Mar 2008
    From
    Canada
    Posts
    1,407
    Nope you're perfectly fine.

    To see why, use the fact that: \sec^2 x = \tan^2 x + 1

    \begin{aligned} \frac{75}{2\cos^2 x} + C & = \frac{75}{2}\sec^2 x + C \\ & = \frac{75}{2} \left(\tan^2 x + 1\right) + C \\ & = \frac{75}{2} \tan^2 x + {\color{red}\frac{75}{2} + C} \end{aligned}

    The stuff in red is nothing more than a constant, so call it K

    So your expression is equal to: \frac{75}{2}\tan^2 x + K

    which is exactly what the book had.

    Remember, all antiderivatives of a given function differ only by their constants which is what we've shown here.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Trig Substitution Integral
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 20th 2009, 09:56 PM
  2. [SOLVED] integration by trig substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 14th 2009, 10:09 PM
  3. [SOLVED] Trig Substitution Integral
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 12th 2009, 08:17 PM
  4. [SOLVED] Using both u and trig substitution
    Posted in the Calculus Forum
    Replies: 14
    Last Post: September 8th 2008, 02:42 PM
  5. [SOLVED] Trig substitution
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 8th 2008, 10:32 AM

Search Tags


/mathhelpforum @mathhelpforum