Jump to content
Sign in to follow this  

Help me on a question on integration!

Recommended Posts

Hi,

 

I've been revising maths HL and now I'm stuck on a question related to integration and substitution? Can anyone help me and teach me how to solve this question?

 

post-145548-0-07385600-1453920429_thumb.

Share this post


Link to post
Share on other sites

Start off by trying to get the integral in terms of tanx somehow. I divided the numerator and denominator by (cosx)^2 to do so. Then, you should have this:

 e1ahzc.png

Since the question said to substitute t=tanx, we can now substitute it. Also, we can substitute dt/dx as (secx)^2. This gives us:

al527n.png

From here, we can do some "tricks" so that we can substitute t=a(tanu), where a is going to be 1/2.

2wr3ghk.png

Finally, we can see that (secu)^2 cancels out with 1+(tanu)^2. This brings us towards the end...

 

2m4t30y.png

 

That should be the answer. Note that, at the end, I just substituted back the values for u and t, and also did some simplification of the radicals along the way.

I'm not sure if this is the best method to solve the question, but this is the way I thought of when I was solving it! I hope I was of some help, and good luck!

Share this post


Link to post
Share on other sites

Start off by trying to get the integral in terms of tanx somehow. I divided the numerator and denominator by (cosx)^2 to do so. Then, you should have this:

Since the question said to substitute t=tanx, we can now substitute it. Also, we can substitute dt/dx as (secx)^2. This gives us:

From here, we can do some "tricks" so that we can substitute t=a(tanu), where a is going to be 1/2.

Finally, we can see that (secu)^2 cancels out with 1+(tanu)^2. This brings us towards the end...

That should be the answer. Note that, at the end, I just substituted back the values for u and t, and also did some simplification of the radicals along the way.

I'm not sure if this is the best method to solve the question, but this is the way I thought of when I was solving it! I hope I was of some help, and good luck!

 

Nicely done! This is a good solution for a good question. Impressive!

Edited by Vioh

Share this post


Link to post
Share on other sites

 

Start off by trying to get the integral in terms of tanx somehow. I divided the numerator and denominator by (cosx)^2 to do so. Then, you should have this:

Since the question said to substitute t=tanx, we can now substitute it. Also, we can substitute dt/dx as (secx)^2. This gives us:

From here, we can do some "tricks" so that we can substitute t=a(tanu), where a is going to be 1/2.

Finally, we can see that (secu)^2 cancels out with 1+(tanu)^2. This brings us towards the end...

That should be the answer. Note that, at the end, I just substituted back the values for u and t, and also did some simplification of the radicals along the way.

I'm not sure if this is the best method to solve the question, but this is the way I thought of when I was solving it! I hope I was of some help, and good luck!

 

Nicely done! This is a good solution for a good question. Impressive!

 

 

oh god, this question was in my december final (or something very similar to it) :( :( . That is a very nice solution!

 

Thank you! While tricky, I'll admit that its solution is very elegant.

Share this post


Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Sign in to follow this  

×
×
  • Create New...