Register to reply 
Quick question about finding area for polar coordinates 
Share this thread: 
#19
Apr3012, 02:01 PM

Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,808




#20
Apr3012, 02:08 PM

P: 235




#21
Apr3012, 02:11 PM

PF Gold
P: 836

[tex]A=\int^b_a \frac{1}{2r^2}\,.d\theta[/tex] Since the OP has confirmed that he got the answer through this interpretation... 


#22
Apr3012, 04:19 PM

P: 54




#23
Apr3012, 04:31 PM

HW Helper
Thanks
P: 10,609

The area of the shaded region is [tex]\int_{3\pi/2}^{2\pi}{\frac{1}{2}r^2d\theta}[/tex]
It is not the same as the integral of [itex]\frac{1}{2r^2}[/itex] over the shaded region. In the second case, the integral is [tex]0.5\int_{\frac{3 \pi} {2}}^{2\pi} \int_0^{\sqrt{\theta}}\frac{1}{r}drd\theta[/tex] ehild 


#24
Apr3012, 05:57 PM

P: 235

My guesses are one of the following (for "he", read "he or she"): a) sharks is winding us up by picking up on an ambiguously written integrand (although I believe it is correctly written) and following through with that to the erroneous solution, in which case he really shouldn't be "confirming" a result that he knows is definitely wrong  especially in a Homework thread; b) sharks believes he is being genuine, but only by the fact that he has assumed that the given integrand is correct (although he has incorrectly misinterpreted it), in which case he really shouldn't be "confirming" a result that he does not know necessarily to be correct  especially in a Homework thread; c) sharks genuinely got it wrong by actually believing his integrand was correct whether he'd read it in the OP or not, in which case he really shouldn't be "confirming" results that he definitely cannot know to be true, as they are not  especially in a Homework thread. I really don't know if it's a or b or c. 


#25
Apr3012, 06:24 PM

PF Gold
P: 836

As far as i'm concerned, the OP didn't write the integral correctly (as he admitted) and anyone could have made the honest mistake of misinterpreting the integrand. If i wasn't sure, i would not have replied, and even if i did, i would have made it clear that i wasn't sure of my suggestion. This is a prime example of why i've grown tired of suggesting to use LaTeX for more clarity, especially when expressions are involved. 


#26
Apr3012, 07:06 PM

P: 235

It's one thing to give hints (that's why my initial replies to you were very short oneliners  I was trying not to give the full answer to you!), but to give an incorrect answer on the basis that you think the provided information was written incorrectly is quite another. (And I still stand by what 1/2r^2 means  even if you think it's ambiguous, you should say so.) I was only trying to correct you as I thought it looked bad to have an incorrect answer from you posted in someone's Homework question. There was no "flaming" intention on my part. Sorry if I gave that impression. 


#27
Apr3012, 07:52 PM

PF Gold
P: 836

Too many times, i've seen people posting in a hurry, with no LaTeX formatting and poor writings of any expression involved. On top of that, they're usually impatient (i assume from having tried several times and failed at reaching an agreeable solution) so they're liable to omit certain little details, like parentheses. So, even though the order of operations does dictate that the expression should be interpreted as [itex]\frac{1}{2}r^2[/itex], i (wrongly) assumed that the OP had skipped the parentheses on purpose. For those who aren't comfortable with LaTeX, parentheses can be crucial in delivering the right question, especially since most people will concentrate on the actual problem, rather than verify if the problem itself has been typed correctly. Example: For a newbie/lazy/careless member posting this: 1/2r^2 could have been 1/(2r^2) or 1/2(r^2). If the OP had used the latter, then the problem would have been really obvious at first sight. Unless everyone starts using LaTeX (or correct use of parentheses) to post their homework, it can be fully expected that this will not be the last time that a "misinterpretation" of an expression in the original problem is at the heart of a wrong suggestion by a homework helper. 


#28
Apr3012, 08:27 PM

P: 235




#29
Apr3012, 08:41 PM

P: 54

Lol, honestly I am new to this forum, so I wasn't even familiar with LaTeX :P. Next time, I'll be sure to use it tho.



#30
Apr3012, 08:46 PM

PF Gold
P: 836




#31
Apr3012, 08:49 PM

P: 235

Even though LaTeX is great for writing out maths, it certainly wasn't necessary for your question. Did you get your answer to be...
Spoiler
[tex]\frac{7}{16}\pi^2[/tex]



#32
Apr3012, 08:58 PM

P: 235




#33
Apr3012, 09:01 PM

P: 54




#34
Apr3012, 09:09 PM

P: 235




Register to reply 
Related Discussions  
Area element in polar coordinates (hard question)  Calculus & Beyond Homework  2  
Quick question on vectors in polar coordinates  Precalculus Mathematics Homework  2  
Polar coordinates finding area between two curves  Calculus & Beyond Homework  9  
Finding area in polar coordinates  Calculus & Beyond Homework  4  
Finding Area in Polar Coordinates  Calculus & Beyond Homework  2 