Facebook Page
Twitter
RSS
+ Reply to Thread
Results 1 to 5 of 5
  1. MHB Master
    karush's Avatar
    Status
    Offline
    Join Date
    Jan 2012
    Location
    Wahiawa, Hawaii
    Posts
    1,477
    Thanks
    1,277 time
    Thanked
    381 times
    #1
    \begin{align*}\displaystyle
    \int_{\alpha}^{\beta}\int_{a}^{\infty}
    g(r,\theta) \, rdr\theta
    =\lim_{b \to \infty}
    \int_{\alpha}^{\beta}\int_{a}^{b}g(r,\theta)rdrd\theta
    \end{align*}
    $\textit{Evaluate the Given}$
    \begin{align*}\displaystyle
    &=\iint\limits_{R} e^{-x^2-y^2} \, dA \\
    (r,\theta) \, 2 \le r \le \infty \\
    &\, 0 \le \theta \le \pi/2
    \end{align*}$\textit{Rewrite with limits}$
    \begin{align*}\displaystyle
    &\lim_{b \to \infty}\int_{0}^{\pi/2}\int_2^{\infty} e^{-x^2-y^2} rdrd\theta
    \end{align*}

    just seeing if I'm going in the right direction☕
    Last edited by karush; September 14th, 2017 at 00:53.

  2. Pessimist Singularitarian
    MHB Coder
    MHB Math Helper
    MHB Ambassador
    MarkFL's Avatar
    Status
    Online
    Join Date
    Feb 2012
    Location
    St. Augustine, FL.
    Posts
    11,982
    Thanks
    32,421 times
    Thanked
    28,356 times
    Thank/Post
    2.367
    Trophies
    24 Highscores
    Awards
    MHB Statistics Award (2016)  

MHB Calculus Award (2016)  

MHB Pre-University Math Award (2016)  

MHB Model Helper Award (2015)  

MHB Calculus Award (2015)
    #2
    What is the problem, exactly as given?

  3. MHB Master
    karush's Avatar
    Status
    Offline
    Join Date
    Jan 2012
    Location
    Wahiawa, Hawaii
    Posts
    1,477
    Thanks
    1,277 time
    Thanked
    381 times
    #3 Thread Author
    Quote Originally Posted by MarkFL View Post
    What is the problem, exactly as given?
    what is b

    frankly I don't know how to finish this

  4. Pessimist Singularitarian
    MHB Coder
    MHB Math Helper
    MHB Ambassador
    MarkFL's Avatar
    Status
    Online
    Join Date
    Feb 2012
    Location
    St. Augustine, FL.
    Posts
    11,982
    Thanks
    32,421 times
    Thanked
    28,356 times
    Thank/Post
    2.367
    Trophies
    24 Highscores
    Awards
    MHB Statistics Award (2016)  

MHB Calculus Award (2016)  

MHB Pre-University Math Award (2016)  

MHB Model Helper Award (2015)  

MHB Calculus Award (2015)
    #4
    Quote Originally Posted by karush View Post
    what is b

    frankly I don't know how to finish this
    You've got an integrand in terms of $x$ and $y$, and differentials in terms of $r$ and $\theta$...can you state the problem exactly as it was given to you?

  5. MHB Journeyman
    MHB Math Helper

    Status
    Offline
    Join Date
    Jan 2012
    Posts
    712
    Thanks
    247 times
    Thanked
    793 times
    Thank/Post
    1.114
    #5
    Of course x2+ y2= r2 so that integral is the same as $ \displaystyle \int_0^{2\pi}\int_2^\infty e^{-r^2}rdrd\theta$. Letting $ \displaystyle u= r^2$, that is easy to integrate.

Similar Threads

  1. Rewriting confusing fractions
    By shamieh in forum Calculus
    Replies: 4
    Last Post: February 28th, 2014, 21:57
  2. Rewriting fractions
    By shamieh in forum Calculus
    Replies: 8
    Last Post: February 20th, 2014, 22:34
  3. [SOLVED] Rewriting a limit as a derivative
    By NavalMonte in forum Calculus
    Replies: 8
    Last Post: February 19th, 2014, 19:02

Tags for this Thread

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  
Math Help Boards