Maths P1-Help Needed!!

[ashutoshamatya]

Integrate y = sec (0.5*x)

 

[ahmed t]

try using the substiution u=sec(0.5x)
but i dont think it will work

 

[ashutoshamatya]

I tried that.. but got mixed up...

 

[ahmed t]

where did u get this question from

 

[anillatoo]

Use the standard formula: Integration(sec x) = ln(sec x + tan x)
I still don't know how to integrate cosec x though...

 

[ahmed t]

i have never heard of this standard integral, are u sure its in our syllabus

 

[XPFMember]

Assalamoalaikum!!

what is this sec..and all that...is it in our syllabus :shock: i've completed the syllabus and pastpapers of P1 but never came across this!! is it a part of our syllabus??

 

[ahmed t]

no its in A2 seems like the one that made this thread got mixed up

 

[XPFMember]

hmmm may be

 

[anillatoo]

I think it is in P3 syllabus, not P1...

 

[ahmed t]

no i checked the syllabus for all p1 p2 p3 and its not there

 

[usman]

http://www.tutorvista.com/math/integrate-cosec-x

 

[anillatoo]

http://www.tutorvista.com/math/integrate-cosec-x

That was brilliant but it is pretty hard to derive the formula for integration, better to remember it with memory.

 

[ahmed t]

its not in our syllabus

 

[Syed.Mazahir.Rizvi]

its p3..only sin,cos and tan identities are in P1

 

[ahmed t]

the intergration of sec and cosec are also not in our syllabus

 

[anillatoo]

yea, it is not in the Maths syllabus actually

 

[usman]

yeah indeed it ain't in the syllabus, bt anyways
1)y = sec(0.5x)
int[y dx] = int[sec(0.5x) dx]
Let u = 0.5x ----> dx = 2du
int[y dx] = 2*int[sec(u) du]
Jux multiply by "sec(u) + tan(u)" above and bottom to get a function(as denominator) with its derivative(as numerator)
= 2*ln[sec(u) +tan(u)] + c
int[sec(0.5x) dx) = 2*ln[sec(0.5x) +tan(0.5x)] + c

2)y = cosec(x)
int[y dx] = int[cosec(x)/1 dx]
Jux multiply by "cosec(x) - cot(x)" above and bottom to get a function(as denominator) with its derivative(as numerator)
int[y dx] = int[cosec(x) dx] = ln[cosec(x) - cot(x)] + c

NB: The values with f(x) = ln(x) are all with modulus sign