Guest SNJERIN Posted March 24, 2015 Report Share Posted March 24, 2015 Hi. So I have been trying to solve this problem but keep ending up with (a=1), hence there would be no area at all. However, the book says that the answer is a= 1+√3, and when you actually test it it does not work. Reply Link to post Share on other sites More sharing options...
ctrls Posted March 24, 2015 Report Share Posted March 24, 2015 (edited) I'm also getting that is the only real solution, so the book seems to be wrong. This result is also is intuitively true, since grows faster than its inverse for , hence it should never be that case past that point that the two integrals are equal. I'm not really sure what the book wants you to do either, I don't see the reason to have two equations for in terms of . Here's my solution, Let be the areas of the pink and blue regions respectively. We can note from the graph that Since we want to solve for a when , by computing we have, Which gives us that , so we conclude that the only solution in the given range is . Edited March 24, 2015 by ctrls Reply Link to post Share on other sites More sharing options...
Guest SNJERIN Posted March 24, 2015 Report Share Posted March 24, 2015 Thanks man. This just confirmed that I am not the only one getting a = 1 every time I try it!! Reply Link to post Share on other sites More sharing options...
Slovakov Posted March 24, 2015 Report Share Posted March 24, 2015 (edited) I haven't done any of these for a long time, so correct me if im wrong. Also I can't believe how long the sheer calculations took me. Im getting old... Edited March 24, 2015 by Slovakov Reply Link to post Share on other sites More sharing options...
Vioh Posted March 24, 2015 Report Share Posted March 24, 2015 I haven't done any of these for a long time, so correct me if im wrong. Also I can't believe how long the sheer calculations took me. Im getting old... You method of derivation is exactly correct. However, you did one algebraic mistake towards the end as: and not Once, you fix this mistake, then , which is nonsense because that would mean that the area doesn't exist. It sucks that math textbooks often have so many errors and typing mistakes, wasting much of our valuable time! Reply Link to post Share on other sites More sharing options...
Slovakov Posted March 24, 2015 Report Share Posted March 24, 2015 (edited) Huh, classic me, you're right. And it looked so beautiful!So if the pink area is always larger, then the exercise really makes no sense... Edited March 25, 2015 by Slovakov Reply Link to post Share on other sites More sharing options...
Guest SNJERIN Posted March 25, 2015 Report Share Posted March 25, 2015 I haven't done any of these for a long time, so correct me if im wrong. Also I can't believe how long the sheer calculations took me. Im getting old... You method of derivation is exactly correct. However, you did one algebraic mistake towards the end as: and not Once, you fix this mistake, then , which is nonsense because that would mean that the area doesn't exist. It sucks that math textbooks often have so many errors and typing mistakes, wasting much of our valuable time! 100% agree with you! and its even more irritating when, after all the practise I have done, I see that my answer didn't agree with the book. However, Its good to see that I was right about my answer from the first attempt. Reply Link to post Share on other sites More sharing options...
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