Results 1 to 7 of 7
Like Tree3Thanks
  • 1 Post By skeeter
  • 1 Post By HallsofIvy
  • 1 Post By skeeter

Thread: Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

  1. #1
    Member
    Joined
    Mar 2017
    From
    Annabay
    Posts
    198

    Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

    y = cos(x), y = 1, −π ≤ x ≤ π


    If i try to solve it finding the integral I get

    $$\int_{-pi}^{pi} cos(x)-1 dx$$


    $$\int_{-pi}^{pi} sin(pi)-(pi) - (sin(-pi) - (-pi)) dx$$

    = -6.283185 which is just 2 x pi and getting rid of the - becomes 6.283185
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,078
    Thanks
    3638

    Re: Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

    Sorry, but I can't read your mind. Is this another area problem? If so ...

    first of all, $1 \ge \cos{x}$

    second, you can take advantage of symmetry ...

    $\displaystyle A = 2\int_0^\pi 1-\cos{x} \, dx$
    Thanks from bee77
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,250
    Thanks
    2838

    Re: Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

    Quote Originally Posted by bee77 View Post
    y = cos(x), y = 1, −π ≤ x ≤ π


    If i try to solve it finding the integral I get

    $$\int_{-pi}^{pi} cos(x)-1 dx$$


    $$\int_{-pi}^{pi} sin(pi)-(pi) - (sin(-pi) - (-pi)) dx$$

    If the problem was to integrate $$\int_{-\pi}^\pi cos(x) -1 dx$$ then your second line is written incorrectly- you have already done the integration, you don't write the integration symbols again:
    $$\int_{-\pi}^\pi cos(x)- 1 dx= \left[sin(x)- x\right]_{-\pi}^\pi= (sin(\pi)- \pi)- (sin(-\pi)- (-\pi))= (0- \pi)- (0+ \pi)= -2\pi$$

    = -6.283185 which is just 2 x pi and getting rid of the - becomes 6.283185
    Why "get rid of the -"?
    Thanks from bee77
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Mar 2017
    From
    Annabay
    Posts
    198

    Re: Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

    I thought with areas we take the absolute value ...is that right ?
    Thanks
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Mar 2017
    From
    Annabay
    Posts
    198

    Re: Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

    Yes another area problem ,sorry .
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    16,078
    Thanks
    3638

    Re: Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

    Quote Originally Posted by bee77 View Post
    I thought with areas we take the absolute value ...is that right ?
    Thanks
    absolute value is required when the curve in question changes sign across the axis ... for the area between curves $f$ and $g$, abs value is required when the curves cross each other and change sign of $f -g$. For a pencil/paper solution, you still have to break it into 2 or more integrals if that happens. If using a calculator with an integrate function, enter the integrand using absolute value over the whole interval.
    Thanks from bee77
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Mar 2017
    From
    Annabay
    Posts
    198

    Re: Should I just try and remember this conceptually ? with cos (x) = 1 or solve?

    Thank you!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Dec 16th 2013, 10:08 AM
  2. Replies: 4
    Last Post: Sep 17th 2010, 02:05 AM
  3. Replies: 4
    Last Post: Apr 16th 2010, 01:24 PM
  4. Can not remember:
    Posted in the LaTeX Help Forum
    Replies: 1
    Last Post: Oct 26th 2008, 02:07 AM
  5. Replies: 1
    Last Post: Jun 26th 2008, 01:38 PM

/mathhelpforum @mathhelpforum