[puttycat1]

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.

[TenOfThem]

Differentiate tan³

[raheem94]

(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,

[hcam]

Can you do integration by parts?

[raheem94]

(Original post by hcam)
Can you do integration by parts?

There is no need to do it.

Just differentiate and see what you get.

[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

[shanban]

sorry didn't realise it was 2x! I'm sure it won't make a huge difference though if you follow the same principle

[finality]

You could do a substitution, let u=tan(2x)

Edit- I was beaten to it. Remember chain rule when finding du/dx.

[puttycat1]

May I ask where the tan^3 2X comes from?

[TenOfThem]

(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

(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

[TenOfThem]

(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

[raheem94]

(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, , so to integrate them, first try to differentiate,

[shanban]

(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?

[TenOfThem]

(Original post by shanban)
/3?

Numerical adjustment

Consider also the 2x

[shanban]

(Original post by TenOfThem)
Numerical adjustment

Consider also the 2x

Oh yes of course, sorry!

[finality]

(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?

[TenOfThem]

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

No ... that is what I said

[finality]

(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

[TenOfThem]

(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