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

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

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- Dec 5th 2008, 07:19 AMAsh_underparSome 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 $\displaystyle \int_0^{2\pi} F(r(t)).r(t)dt$ - Dec 6th 2008, 01:17 AMCaptainBlack
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 - Dec 7th 2008, 06:25 AMAsh_underpar
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!