Probably easy--integration (1 Viewer)

[Roobs]

hey all heres a question.....

this is from Fitz. 33f Q41 part iv for those who have the book...but anyway

verify by differentiation:

n∫cos^n x dx = sinxcos^(n-1) x +(n-1) ∫ cos^(n-2) x dx. (straightforward)

hence evaluate

∫ sec^4 x dx between (Pi/4) and 0

(answer is 4/3)

i can do the question with trig substitution but the HENCE part has got me stumped......

 

[hyparzero]

hint:

∫ sec⁴(x)dx = ∫ cos^-4(x)dx

 

[Roobs]

yeah but wont you then just be trying to solve:

-5∫cos^(-6) x dx.

???

 

[_ShiFTy_]

Hint:

Make ∫ cos^(n-2)x dx the subject

 

[Roobs]

tricky bastard lol...i think i got it now...but i'll be back if i dont lol