Q on reduction formula.

I tried it but it hasnt work. The du/dx also doesnt work as I am getting the same ans the before and you think its incorrect. I cant think of doing this differently. I really cant do this Q, i will ask the teacher for ans.
 
The reduction proof is not that bad at all. Just use integration by parts. To make our life easier, especially if you make a mistake, please state all your substitutions (u=?, v =? du=? and dv=?). This really makes things easier for the helpers as we can then see your mistake more easily. Try again and take it slow.
 
Sonal7 said:
I tried it but it hasnt work. The du/dx also doesnt work as I am getting the same ans the before and you think its incorrect. I cant think of doing this differently. I really cant do this Q, i will ask the teacher for ans.
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No, please don't give up. You can do it. Please try again and we'll help you through it.
 
For the record the first thing that I would do is let u=2x. This way the angle would be easy to work with.
 
its too hard. i have tried so many days. I dont think its good to reinforce wrong stuff. I think i cant do it then I cant do it.
 
unless you think i should use law of indices. I think n x In might and -1 x I n+1. I am splitting up (n-1) term.
 
That was hard. I would not have got to it. I got where i made the mistake in differentiation. Yes that was silly. Good question I think
 
What you need (and we all need) is patience in checking. As I said before, check every single thing you write, because silly mistakes happen to all of us. Think of every integration problem as also providing practice in differentiation (and algebra, and ...), and check each step as if it were a test problem! You're right that it is not good to reinforce errors; so you must catch every error before you repeat it.

With practice, and not giving up, you will eventually make fewer silly mistakes, and catch more of them. But don't practice giving up.

I'll repeat something I've said to many students: To prevent silly mistakes,
  1. Think -- never do even the smallest bit of math with your mind turned off because it is so easy.
  2. Write what you thought -- while it is still in your mind, it is easy to do it wrong.
  3. Think about what you wrote -- when it is visible, you can compare it to the previous line and to known facts.
  4. Fix it! -- because that will still be needed from time to time even when you are an expert.
(I recently wrote a blog post quoting something written (informally) by the great mathematician John Conway, and in proofreading it, I found that he had made a mistake -- because he didn't write out his work! It literally does happen to the best of us.)
 
I did give up when i was nearly there. I didnt spot the mistake. I will look into your blog, it sound interesting. I also came across something incredibly good on studying maths on the web. Its about how the mind works and it is solving problems when you think it is not. So if you walk away from something, and come back to it you might solve it. Also changing topics. That was a bit hard I thought. I felt really beaten by this Q. I shouldnt felt that way, after all I might have kept eliminating the different options that was not working and thus come to the answer. I might have been able to use logic to work out which bit wasnt working. Thanks for the encouragement.
 
It is definitely true that stepping away from a problem can help. Your mind can get stuck, and thinking about other things (or literally taking a walk) can free you up and give you a new perspective (or maybe even a solution will come to you as you walk even though you are deliberately not thinking consciously about it). Of course, walking away for a while is not giving up! It's just being human.
 
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