need help URGENTLY!! (1 Viewer)

[Pace_T]

Integrate:
S(cosec^2(x))dx

A = -cot(x) + c

S(cosec(x)cot(x))dx

A = -cosec(x) + c

S(sec(x)tan(x))dx

A = sec(x) + c

These are common rules i think, but im pretty sure my teacher will put 1 of them in the halfy tomorrow!!! (unless these don't have to be proven? but i cannt be sure though). i know ive been asking alot of q's recently but my half yearly is just coming up, ill help as much as i can in return!
somone please help!! thank you!

 

[richz]

why dont u just remember them??? even u said they are common rules.... :rollyeyes:

 

[KFunk]

Integrate:
S(cosec^2(x))dx

A = -cot(x) + c

S(cosec(x)cot(x))dx

A = -cosec(x) + c

S(sec(x)tan(x))dx

A = sec(x) + c

These are common rules i think, but im pretty sure my teacher will put 1 of them in the halfy tomorrow!!! (unless these don't have to be proven? but i cannt be sure though). i know ive been asking alot of q's recently but my half yearly is just coming up, ill help as much as i can in return!
somone please help!! thank you!

I assume you want to know how to prove them? Working backwards:

∫ secx.tanx dx
= ∫ (cosx)^-2.sinx dx let u=cosx ---> du = -sinxdx
= - ∫ u^-2 du
= -(-1/u) = 1/cosx = secx + c

∫ cosecx.cotx dx
= ∫ (sinx)^-2.cosx dx let u=sinx ---> du=cosxdx
=∫ u^-2 du
= -1/u = -cosecx +c

 

[KFunk]

∫ cosec²x dx
= ∫ cot²x.sec²x dx
= ∫ (tanx)^-2.sec²x dx
let u = tanx ---> du = sec²xdx

= ∫ u^-2 du
= -1/u = -1/tanx = -cotx +c

 

[Slidey]

This is 4unit, just so you know, Pace.

 

[Pace_T]

thanks all, you people are so helpful
oh, i *think* they are common rules, but none the less, my teacher is a nutcase, he'll put in any sorts of questions cause he's a gaybo.
LOL
thanks