Results 1 to 2 of 2

Math Help - why is this equal to zero?

  1. #1
    Senior Member
    Joined
    May 2012
    From
    Toronto
    Posts
    253
    Thanks
    1

    why is this equal to zero?

    why is this equal to zero?-screen-shot-2012-12-13-9.46.36-pm.png
    sorry it's not equal to zero, I was looking at the wrong answer:


    I tried using the f'(t)h(f(t) - g'(t)h(g(t)) method but I got

    2sinx cosx(csc^2x+sec^x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member x3bnm's Avatar
    Joined
    Nov 2009
    Posts
    300
    Thanks
    16

    Re: why is this equal to zero?

    You can solve it like this:

    \begin{align*} \frac{d}{dy}\int_{\cos^{2}(y)}^{\sin^{2}(y)}\frac{  1}{t} dt  =& \frac{d}{dy}\left( \ln(t) \Big{|}^{\sin^{2}(y)}_{\cos^{2}(y)}\right) \\ =& \frac{d}{dy}[\ln{(\sin^{2}(y))} - \ln{(\cos^{2}(y))}] \\ =& \frac{2 \sin(y) \cos(y)}{\sin^{2}(y)} + \frac{2 \sin(y) \cos(y)}{\cos^{2}(y)} \\ =& \frac{2\sin(y)\cos^{3}(y) + 2\sin^{3}(y)\cos(y)}{\sin^{2}(y)\cos^{2}(y)} \\ =& \frac{2\sin(y)\cos(y)(\sin^{2}(y) + \cos^{2}(y))}{\sin^{2}(y)\cos^{2}(y)} \\ =& \frac{2\sin(y)\cos(y)}{\sin^{2}(y)\cos^{2}(y)} \\ =& 2\csc(y)\sec(y) \end{align*}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 11th 2012, 05:21 PM
  2. Equal power sets -> Equal sets?
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: July 5th 2012, 10:23 AM
  3. Replies: 6
    Last Post: May 14th 2011, 07:12 PM
  4. [SOLVED] Is it really equal? Why?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 7th 2010, 12:51 PM
  5. Replies: 2
    Last Post: March 23rd 2009, 08:11 AM

Search Tags


/mathhelpforum @mathhelpforum