Integrate Spiral on YZ Plane | Location X | Need Help with Problem

[starbaj12]

There is a spiral but it is just on the yz plane (no length to it) I need to integrate it. And I'm at a location x on the axis if it matters.

Thanks

 

[ReyChiquito]

What do you want to calculate? its lenght? if so, let M(t) be your curve, as long as M'(t) \ne 0 then

Length[M]=\int_{t_0}^{t_1} \sqrt{\dot{x}^2+\dot{y}^2+\dot{z}^2}ds

 

[starbaj12]

alpha; which is the angle subtended by a radius at the point of observation (x).

 

[HallsofIvy]

I'm sorry but I can't make heads or tails of this.

"There is a spiral but it is just on the yz plane (no length to it) I need to integrate it."
?? You can't integrate a spiral, you can only integrate a function.

"alpha; which is the angle subtended by a radius at the point of observation (x)."

What about alpha? A single line does not "subtend" an angle. And what is the "point of observation"?

 

[pete1141]

What does "subtend " mean ? Can't you mathematicians puy it in words ordinary people can understand . Also "leght " is spelled "length". The expression is "head or tail "for a single event not "heads and tails ". You mathematicians are so precise in everything except the lagauge used to express your ideas .

 

[pete1141]

Sorry "put" not puy (slip of the finger )

 

[starbaj12]

The spiral has a center in the yzx axis (it is like a coil but flat so the radius gets bigger) You can do this by polar coordinates (I was told), but I do not know how. I need to find a vector field that is directed along the x axis. And alpha is the angle subtended by a radius at the point on x.

 

[600burger]

What does "subtend " mean ? Can't you mathematicians puy it in words ordinary people can understand . Also "leght " is spelled "length". The expression is "head or tail "for a single event not "heads and tails ". You mathematicians are so precise in everything except the lagauge used to express your ideas .

He used "subtend" perfectlly...if it were a helix, but its a spiral, so there is no angle. The rest of your complaint is about typos and dialects, which is pointless to get mad about.

starbaj12, I think you'll need to be more specific in your request for help.

-Burg

 

[Captain Cool Guy]

Line integrals of three space

You can find it by parameterizing the curve. Spirals are pretty easy to parameterize and would be similar to: x=cos(t) y=sin(t) z=t. Then you can take the integral from start to finish of f(x(t),y(t))|ds|dt. You can find this by looking in the index of any calculus book under line integrals in 3-space or something similar. This isn't usually done until Calculus III, so it would be towards the back of the book.

 

[ReyChiquito]

also, as halls of ivy just said, you can't go integrating blindly, you need to do it by pieces (where the length is well defined, M'(t)\ne 0)