Integration question (1 Viewer)

[wilsondw]

How do you integrate from 0 to Pi 1/(5-4cosx) dx

It may seem like a silly question

EDIT: problem is that when I use T method...subbing pi into tan(x/2)=tan(pi/2) which is undefined

 

[Aysce]

Let t = tan(x/2)

Differentiate t WRT x to find dx.

So since we let t = tan(x/2), using t-results, we know cos is 1-t^2 over 1+t^2

Follow on from that. I can't use latex

 

[wilsondw]

I know that...its just when u let t=tan(x/2) and sub in pi....it is undefined

 

[nightweaver066]

I don't know if you're allowed to do this or not but use infinite as the upper limit after substitution.

It gets you the answer lol.

 

[funnytomato]

I doubt that's gonna appear in any of your school assessments or the hsc

but it's quite intuitive to understand the idea of an improper integral

this is an example:

in your particular question, we should get(after doing the substitution) :

 

[Trebla]

You can work your way around the problem using a substitution



The integral then becomes



which allows you to proceed as usual...

 

[wilsondw]

THANKS FOR THE HELP GUYS!..really appreciate it!

 

[funnytomato]

You can work your way around the problem using a substitution



The integral then becomes



which allows you to proceed as usual...

this is very neat
wish I could rep

 

[funnytomato]

'You must spread some Reputation around before giving it to Trebla again.'

 

[Alkenes]

So is that in the 4unit syllabus?

 

[Alkenes]

Guys when we have integration question in which we have to make t=tan(x/2) and we have limits, do we change the limits or just sub the original in the answer?

 

[Nooblet94]

Guys when we have integration question in which we have to make t=tan(x/2) and we have limits, do we change the limits or just sub the original in the answer?

Either way works, although personally I find changing limits is easier and quicker. Just make sure that if you're not changing limits to evaluate the integral as an indefinite integral first, because if you leave the limits there but make the substitution not only will you confuse yourself, but it's also entirely wrong.