ebu Posted January 27, 2016 Report Share Posted January 27, 2016 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? 1 Reply Link to post Share on other sites More sharing options...
isaiguana Posted January 27, 2016 Report Share Posted January 27, 2016 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! 6 Reply Link to post Share on other sites More sharing options...
Vioh Posted January 28, 2016 Report Share Posted January 28, 2016 (edited) 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 January 28, 2016 by Vioh Reply Link to post Share on other sites More sharing options...
eross Posted January 28, 2016 Report Share Posted January 28, 2016 oh god, this question was in my december final (or something very similar to it) :( . That is a very nice solution! Reply Link to post Share on other sites More sharing options...
isaiguana Posted January 28, 2016 Report Share Posted January 28, 2016 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. Reply Link to post Share on other sites More sharing options...
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