Results 1 to 8 of 8

Math Help - Find the length of the curve

  1. #1
    Newbie
    Joined
    Jan 2014
    From
    USA
    Posts
    4

    Find the length of the curve

    Find the length of the curve r=\frac{e^\theta}{\sqrt2} on the interval 0\leq\theta\leq\pi. I've plugged everything into the equation, but I can't seem to get the same answer that is on the answer sheet, which is e^\pi-1.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,656
    Thanks
    1065

    Re: Find the length of the curve

    the answer is e^{\pi-1} not (e^\pi - 1) as you've written.

    does that help any?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2014
    From
    USA
    Posts
    4

    Re: Find the length of the curve

    No, could you go over it step-by-step?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,674
    Thanks
    1498

    Re: Find the length of the curve

    Do you have a rule that you can follow to find the arclength of a polar curve?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2014
    From
    USA
    Posts
    4

    Re: Find the length of the curve

    Yes, the equation is L=\int_{a}^{b}\sqrt{r^2+(\frac{dr}{d\theta})^2.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,674
    Thanks
    1498

    Re: Find the length of the curve

    Well then, what is your \displaystyle \begin{align*} r^2 \end{align*} and \displaystyle \begin{align*} \left( \frac{dr}{d\theta} \right) ^2 \end{align*}? What are your a and b?

    Also, the equation is actually \displaystyle \begin{align*} L = \int_a^b{\sqrt{r^2 + \left( \frac{dr}{d\theta} \right) ^2 }\,d\theta} \end{align*}...
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jan 2014
    From
    USA
    Posts
    4

    Re: Find the length of the curve

    r^2=\frac{dr}{d\theta}=\frac{e^{\theta}}{\sqrt{2}}; a=0; b=\pi
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    2,656
    Thanks
    1065

    Re: Find the length of the curve

    Quote Originally Posted by accountholder View Post
    r^2=\frac{dr}{d\theta}=\frac{e^{\theta}}{\sqrt{2}}; a=0; b=\pi
    no.

    you are given r=\frac{e^\theta}{\sqrt{2}}

    so r^2=\frac{e^{2\theta}}{2}

    \frac{d^2r}{d\theta^2}=\frac{dr}{d\theta}=\frac{e^  \theta}{\sqrt{2}}

    so \left(\frac{d^2r}{d\theta^2}\right)^2=\frac{e^{2 \theta}}{2}

    now take your arc length formula and do the integration. Your limits are correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the length of the curve
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 29th 2010, 10:21 AM
  2. Trying to find the length of a curve.
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: February 13th 2010, 05:20 AM
  3. Find the length of the curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 6th 2009, 08:56 AM
  4. find length of curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 15th 2009, 04:55 PM
  5. Find length of the curve help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 4th 2008, 09:15 PM

Search Tags


/mathhelpforum @mathhelpforum