/sci/ - Science & Math

So should you

But I(U) isn't a function, its a definite value isn't it?

I mean, it goes from 0 to pi

>>5077013
I(u) = f(x) = Left as an exercise to the reader

>>5077031
Yes, I(u) in OPs case would evaluate to a definite value, unless OP is considering pi as a variable

>>5077031
>>5077040

PROTIP: dx

>>5077043
>PROTIP: dx
You're still running it as a definite integral which is a real value, not a function

It will come out to I(U) = C, where C is a constant

>>5077031
Do you know what a function is? A single value is a perfectly adequate function.

>>5077049
>OP asks /sci/ to evaluate an integral
>/sci/ doesn't even understand how integrals work

Simplify as far as possible (n is a positive integer)
<span class="math">\int_0^{2\pi}e^{\cos\theta}\cos(\sin\theta-n\theta)d\theta[/spoiler]

>>5077053
but you and I both know thats not what OP wanted

>>5077057
>>/sci/ doesn't even understand how integrals work
The integral from 0 to 1 of x(dx) is 1/2

Not x^2/2, just 1/2

When you have a definite integral, you get a value, not a function
>a value can be a function
A function that actually does something then

>>5077031
>>5077040
>>5077049
>>5077053

This is a definite integral:

<div class="math"> \int_0^1 ux dx = \left. \frac{ux^2}{2} \right|_0^1 = \frac{u}{2}</div>

<span class="math">u/2[/spoiler] is not a real number.

>>5077074
No one asks questions as found in OP, don't worry.

>>5077013
> decided to take the spring and summer semester off
> signed up for multivariate calculus for next semester
> semester starts on Monday

> tfw I forgot all my calculus

>>5077076
just assume `u' is a constant and integrate the function with respect to x.

>>5077071
I suppose this is correct.

I'm thinking about it all wrong

>>5077079
>just assume `u' is a constant and integrate the function with respect to x.
Well then that seems to make the problem a lot easier, though the algebra probably still looks messy.

>>5077013

to give you an idea of the complexity involved in finding the antiderivative...
http://www.wolframalpha.com/input/?i=integral+of+ln%28cosx%29dx

and the additional terms are just going to add complexity to that. i don't think there is an easy way to do this by hand.

>>5077105

I was hoping there was some sort of nice trick to it, like writing u^2 - 2ucos(x) + 1 as (u-cos(x))^2 + sin^2(x), but that didn't really help much. I guess it's difficult when we don't know what we're meant to be treating U as.

Guys, real quick question here: (Fx,Fy,-1) is a normal vector for an arbitrary F(x,y) why is it -1?

>>5077139
>F(x,y)
What is this

>>5077164

An arbitrary function in R3, scalar valued, where Fx = dF/dx

>>5077139
The tangent from the y direction is (0,1,Fy).
The tangent from the x direction is (1,0,Fx).
The cross product of them is (Fx,Fy,-1)

>>5077195

No shit, huh? Well that was obvious, thanks bro.