Results 1 to 2 of 2

Math Help - Find the area of a petal sketch.

  1. #1
    Newbie
    Joined
    Mar 2011
    Posts
    7

    Find the area of a petal sketch.

    Find the area of a petal sketch.
    1) r= 4 sin(2theta)
    2) r= 4sin(theta)
    3) Compare and contrast conjecture.


    Please please please help me with this calculus problem. I am so lost in my class. step by step work would be greatly appreciated. The work does not have to be completely accurate, I just need the steps. Thank you in advance.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,692
    Thanks
    450
    Quote Originally Posted by mymony1027 View Post
    Find the area of a petal sketch.
    1) r= 4 sin(2theta)
    2) r= 4sin(theta)
    3) Compare and contrast conjecture.


    Please please please help me with this calculus problem. I am so lost in my class. step by step work would be greatly appreciated. The work does not have to be completely accurate, I just need the steps. Thank you in advance.
    help with #1 ... know how to sketch a polar graph? if not, you need to relearn how ... it's critical for determining area of a polar graph.

    note that one petal gets formed for r = 4\sin(2\theta) by values of \theta , 0 \le \theta \le \dfrac{\pi}{2}

    using the form for area of polar curves ... \displaystyle A = \int_{\theta_1}^{\theta_2} \frac{r^2}{2} \, d\theta ...

    \displaystyle A = \int_{0}^{\frac{\pi}{2}} 8\sin^2(2\theta) \, d\theta

    use the power reduction identity ...

    \sin^2(2\theta) = \dfrac{1 - \cos(4\theta)}{2} to help in the integration.

    \displaystyle A = 4\int_{0}^{\frac{\pi}{2}} 1 - \cos(4\theta) \, d\theta

    4\left[\theta - \dfrac{\sin(4\theta)}{4}\right]_0^{\frac{\pi}{2}}

    4\left[\dfrac{\pi}{2} - 0\right] = 2\pi

    o.k. you try #2.
    Attached Thumbnails Attached Thumbnails Find the area of a petal sketch.-polar10.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sketch the set Ta and find its area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 4th 2010, 04:03 PM
  2. Sketch the region and find the area.
    Posted in the Calculus Forum
    Replies: 11
    Last Post: June 1st 2010, 11:04 AM
  3. Area of a rose petal using Green's Theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 23rd 2010, 09:02 AM
  4. Sketch the region and find the area
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 9th 2009, 10:59 PM
  5. Sketch Area
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 19th 2007, 12:51 AM

Search Tags


/mathhelpforum @mathhelpforum