A350XWB wrote:
I'm at odds with my calculus II teacher because of this integral: -4/(1+X^2) DX.
My teacher says it's -4 arc tan X + C while I say it is 4 arc cotan X + C.
Anyone can help me?
You are, of course, both right.
The angle whose tangent is "x", is pi/2 - (the angle whose cotangent is "x").
Just think of a right-angled triangle.
I.e arc cotan X = pi/2 - arc tan X.
Hence the two solutions you give above do indeed just say exactly the same thing, bar for the choice of constant "C".
Now, as to which one of you is "more right"... I'd side with your teacher, to a tiny degree. Although they have to have a minus sign in their version of the solution, in general usage, the arc tangent is the "preferred" function. It mainly a matter of taste.
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Last edited by lau on 01 May 2008, 2:06 pm, edited 1 time in total.