# Thread: Some Form of integral question! who knows

1. ## Some Form of integral question! who knows

Let $\displaystyle F=[2 \sin (x) \cos (x), 0, 2z]$ and $\displaystyle r(t)=[\cos (t),\sin (t),t]$

Calculate $\displaystyle \int_0^{2\pi} F(r(t)).r(t)dt$

2. Originally Posted by Ash_underpar
Let $\displaystyle F=[2 \sin (x) \cos (x), 0, 2z]$ and $\displaystyle r(t)=[\cos (t),\sin (t),t]$

Calculate $\displaystyle \int_0^{2\pi} F(r(t)).r(t)dt$
I'm not sure your notation makes sense as it is. $\displaystyle F$ is a function of two(?) (real?) variables taking values in $\displaystyle \mathbb(R)^3$, and $\displaystyle r$ is a function of a single (real?) variable taking values in $\displaystyle \mathbb(R)^3$, so $\displaystyle F(r(t))$ is not properly defined. I expect with a bit of effort we could make some sort of guess about what this is supposed to denote but it would be better if you sorted it out.

CB

3. Originally Posted by CaptainBlack
I'm not sure your notation makes sense as it is. $\displaystyle F$ is a function of two(?) (real?) variables taking values in $\displaystyle \mathbb(R)^3$, and $\displaystyle r$ is a function of a single (real?) variable taking values in $\displaystyle \mathbb(R)^3$, so $\displaystyle F(r(t))$ is not properly defined. I expect with a bit of effort we could make some sort of guess about what this is supposed to denote but it would be better if you sorted it out.

CB
I figured that F(r(t)) could be worked out by using the vector format and taking xi,yj,zk to equal the values of the three points of r(t) taking the y value as 0y, and then integrate the dot product between this value and r(t), which is what i am stuck on but the question i have been set is written exactly as i have put on here.

In textbooks i have used, F seems to be denoted by F(r), but i don't know if thats actually a completely separate value!