Hi im having trouble on where to start, im trying to itegrate sin(x)/cos^2(x). Should i make a u subsitution, if so for what?
I have had several tell me that in Europe they do not deal with sec,csc,cot at all.
Wonder why?.
For your benefit. Their derivatives:
$\displaystyle \frac{d}{dx}[csc(x)]=-cot(x)csc(x)$
$\displaystyle \frac{d}{dx}[cot(x)]=-csc^{2}(x)$
$\displaystyle \frac{d}{dx}[sec(x)]=tan(x)sec(x)$
In France, we've never seen such formulae... Only dealing with cos, tan, sin, and that was enough ^^ (in my high school...can't tell about all the others). Why ? I don't know, maybe because cot, csc, sec are known with sin, cos, tan... ~
It's the same for the substitution. It seems that for you it's common to substitute, but here, we just recognize the derivative and apply formulae of antiderivatives we know
Actually, by "here" in my previous post, I meant the equality of Chris where an antiderivative of sec*tan is sec..
Edit : thanks a bunch !
I reckon that's so. Same reason most calculators do not have them.Why ? I don't know, maybe because cot, csc, sec are known with sin, cos, tan... ~
One thing I noticed about calculators that do have them (such as the Voyage 200, TI-92, TI-89), they have the functions but only display in terms of sine and cosine. For instance, if you wanted the antiderivative of sec(x), the calculator displays it as $\displaystyle ln(\frac{-cos(x)}{sin(x)-1})$ instead of
$\displaystyle ln(sec(x)+tan(x))$