Trig Integration question - is both methods acceptable? (1 Viewer)

[clintmyster]

Have a look at my working out below for the same question. When I evaluate the integrating using mathematica, I get the -cot^2x/2 answer. I'm wondering though is the other method wrong and if so how is it? Thanks heaps

 

[GUSSSSSSSSSSSSS]

its all fine

as (cotx)^2 and (cosecx)^2 only differ by a constant:

(cotx)^2 + 1 = (cosecx)^2


you get??

 

[jet]

since cosec^2 = 1 + cot^2 you will find that they only differ by the constant. So either method is equally valid.

 

[clintmyster]

Oh thanks guys, I never realised that! wow. That'd mean if you had a definite integral it should be the same answer for both methods?

 

[GUSSSSSSSSSSSSS]

haha we posted up answers at like same time lol


but yes thats exactly wat it means
thats why trig integration is very weird, as depending on wat method you use u often come up with different solutions
so dun always rely on the answer in the back of the book lol...

 

[clintmyster]

haha we posted up answers at like same time lol


but yes thats exactly wat it means
thats why trig integration is very weird, as depending on wat method you use u often come up with different solutions
so dun always rely on the answer in the back of the book lol...

this was posted up by some guy in the 2unit section to do it just by inspection but seeing as i hate inspection i just did it by substitution.
Thanks again

 

[gurmies]

I only use inspection for these types of questions =(

 

[Trebla]

Oh thanks guys, I never realised that! wow. That'd mean if you had a definite integral it should be the same answer for both methods?

haha we posted up answers at like same time lol


but yes thats exactly wat it means
thats why trig integration is very weird, as depending on wat method you use u often come up with different solutions
so dun always rely on the answer in the back of the book lol...

They would always give the same solution, regardless of what method you use. If they differ by a constant, then it doesn't change the main primitive function because that constant can be incoroprated in the "+ c" when writing out the integral. In terms of a definite integral, any constants would cancel each other out.
e.g.