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C4 integration Question

Hiya, I'm having abit of trouble integrating the following term between the limits of 0 and Pie/6.

Y=Sec22X Tan22X


Thanks for any help.
Reply 1
Differentiate tan3
Reply 2
Original post by puttycat1
Hiya, I'm having abit of trouble integrating the following term between the limits of 0 and Pie/6.



Thanks for any help.


Understand the difference between 'pi' and 'pie'.

For solving the question, try differentiating, tan32x tan^32x
Reply 3
Can you do integration by parts?
Reply 4
Original post by hcam
Can you do integration by parts?


There is no need to do it.

Just differentiate tan32x tan^32x and see what you get.
Reply 5
use the substitution u=tanx, then dx=1/sec^2x.du and this cancels so you're left with the integral of u^2, remember to change your limits though :smile:
Reply 6
sorry didn't realise it was 2x! I'm sure it won't make a huge difference though if you follow the same principle :smile:
Reply 7
You could do a substitution, let u=tan(2x)

Edit- I was beaten to it. Remember chain rule when finding du/dx.
(edited 11 years ago)
Reply 8
May I ask where the tan^3 2X comes from?
Reply 9
Original post by shanban
use the substitution u=tanx, then dx=1/sec^2x.du and this cancels so you're left with the integral of u^2, remember to change your limits though :smile:



Original post by finality
You could do a substitution, let u=tan(2x)



I find it interesting that people advocate substitution ... in order to spot this you would need to spot that sec2 is the derivative of tan ... then if you spot that why don't you just see that it is tan3 with a bit of numerical adjustment
Original post by puttycat1
May I ask where the tan^3 2X comes from?


the fact that sec2 is the derivative of tan

and an understanding of the chain rule
Reply 11
Original post by puttycat1
May I ask where the tan^3 2X comes from?


It is just a technique of integration.

Sometimes integrals are of the type, f(x)(f(x))n dx \displaystyle \int f'(x)(f(x))^n \ dx , so to integrate them, first try to differentiate, (f(x))n+1 (f(x))^{n+1}
Reply 12
Original post by TenOfThem
I find it interesting that people advocate substitution ... in order to spot this you would need to spot that sec2 is the derivative of tan ... then if you spot that why don't you just see that it is tan3 with a bit of numerical adjustment


yeah I suppose, just easier to get the method marks with the other method?

Also wouldn't it be (tan^3)/3?
Original post by shanban
/3?



Numerical adjustment

Consider also the 2x
Reply 14
Original post by TenOfThem
Numerical adjustment

Consider also the 2x


Oh yes of course, sorry!
Reply 15
Original post by TenOfThem
I find it interesting that people advocate substitution ... in order to spot this you would need to spot that sec2 is the derivative of tan ... then if you spot that why don't you just see that it is tan3 with a bit of numerical adjustment


But the integral here is (tan32x)/6
or am I missing something?
Original post by finality
But the integral here is (tan32x)/6
or am I missing something?


No ... that is what I said
Reply 17
Original post by TenOfThem
No ... that is what I said


Oh, is that what you meant by numerical adjustment? I thought you were saying it was just tan32x
Original post by finality
Oh, is that what you meant by numerical adjustment? I thought you were saying it was just tan32x


Aaaaah ... no

My point was

Spot that it is tan cubed and adjust as needed :smile:

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