Integration by Substitution help needed please (2 Viewers)

[funnytomato]

The strict definition of cot x is NOT 1/tan x. The definition of cot x is in fact (cos x)/(sin x) and it is only equal to 1/tan x if tan x is defined.

for ALL these years, my maths teacher has been lying !!!
but a good point

 

[kooliskool]

Erm, is this really a high school maths question? Boundaries with infinite is suppose to be in uni isn't it......

 

[Omnipotence]

there are many ways to integrate cosec x
I would just multiply it by (cosec x +cot x )/(cosec x +cot x)

then factorise -1 at the front, then it becomes a log

Yep, this is the method I use. Similar for secx aswell, multiply denominator and numerator by (secx + tanx).

 

[XTsquared]

They can ask you questions involving infinite limits. They're not that difficult to answer since generally the graph of the function will have a limiting value (ie horizontal asymptote), so the area under the curve has a finite value. If that made any sense.

 

[Deep Blue]

but isnt that involving limits and such? I mean, the exact value of tan pi/2 is undefined... or is it infinity??

It is undefined because it approaches infinity at that point. Are you familiar with how asymptotes work?