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anonymous
 4 years ago
Let F(r)=(2y,z,x);calculate integer F(r) x dr?
let F(r)=(2y,z,x);calculate integer F(r) x dr along the curve x=cost,y=sint,z=2cost from t=0 to t= pi/2....
anonymous
 4 years ago
Let F(r)=(2y,z,x);calculate integer F(r) x dr? let F(r)=(2y,z,x);calculate integer F(r) x dr along the curve x=cost,y=sint,z=2cost from t=0 to t= pi/2....

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TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.1I'm going to assume a lot of things since this is typed strangely. I'm assuming you want the line integral of the vector field F along the given curve.\[\int_{a}^{b}\overrightarrow{F}(r)\cdot d\overrightarrow{r}=\int_{a}^{b}\overrightarrow{F}(\overrightarrow{r}(t))\cdot \overrightarrow{r'}(t)\]so we need the parameterization of our vector function.\[\overrightarrow{F}(\overrightarrow{r}(t))=<2y(t),z(t),x(t)>=<2\sin t,2\cos t,\cos t>\]and we need the derivative of the curve\[\overrightarrow{r'}(t)=<\sin t,\cos t,2\sin t>\]out integrand will be the dotproduct if these two vector quantities.\[\int_{a}^{b}\overrightarrow{F}(\overrightarrow{r}(t))\cdot \overrightarrow{r'}(t)dt\]\[=\int_{0}^{\pi/2}<2\sin t,2\cos t,\cos t>\cdot<\sin t, \cos t,2\sin t>dt\]So now just take the dotproduct and integrate.
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