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MathSofiya
Group Title
Evaluate the line integral \[\int_c F\cdot dr\] where c is the vector function
\[\hat{r}(t)=t^3\hat it^2 \hat j+ t \hat k\]
and
\[F(x,y,z)=sinx\hat i + cosy \hat j+zx \hat k\]
Here is how far I have gotten so far:
\[\hat{r}'(t)=3t^2\hat i2t \hat j+ \hat k\]
 2 years ago
 2 years ago
MathSofiya Group Title
Evaluate the line integral \[\int_c F\cdot dr\] where c is the vector function \[\hat{r}(t)=t^3\hat it^2 \hat j+ t \hat k\] and \[F(x,y,z)=sinx\hat i + cosy \hat j+zx \hat k\] Here is how far I have gotten so far: \[\hat{r}'(t)=3t^2\hat i2t \hat j+ \hat k\]
 2 years ago
 2 years ago

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lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
you might want to use \cdot rather than \bullet hehe
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
I'll change the Function F in terms of t's in just a second
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
thanks @lgbasallote. Better? :P
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
yes. yes it is.
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
oh my, I did I similar problem 28 days ago http://openstudy.com/study#/updates/50060b97e4b06241806745b8 and I'm also looking at http://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsVectorFields.aspx but I can't seem to remember... What do i substitute in for x and y, do I pick which one I want t to be?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
Hey i think I got it! \[x=t^3;y=t^2;z=t\] YES?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
That would give me: \[F(r(t))=sin(t^3)\hat i +cos(t^2)\hat j+t^4 \hat k \]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
\[\int_{t=0}^{t=1}\left(sin(t^3)\hat i +cos(t^2)\hat j+t^4 \hat k\right)\cdot\left(3t^2\hat i 2t\hat j +\hat k \right) dt\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
and now I would just do the dot product correct?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
\[\int_0^1(3t^2sin(t^3)2tcos(t^2)+t^4)dt\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
wait, I have to take the integral of several products?
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
separate them\[\int_{0}^{1} 3t^2 \sin t^3 dt+...+...\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
oh ok \[\int_0^1 3t^2sin(t^3)dt\int_0^12tcos(t^2)dt+\int_0^1t^4dt\] like this?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
oh integration by parts! duh =D
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
\[\cos t^3\] :)
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
no integration by parts you can do it all with usubs
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
do you get that?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
Oh I see it now!!!!
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
u=t^2 du=2t dt for the second integral
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
u=t^3 and du=3t^2 dt for the first integral...LOL that took me a while!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
yeah, it's well setup for the usub thing :)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
u cooked the problem
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
\[cos(1)+sin(1)+2\] My algebra is probably wrong...but Yeah @mukushla that was one long recipe!
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
\[\large \cos t^3]_{0}^{1}+\sin t^2]_{0}^{1}+t^5/5]_{0}^{1}\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
\[(cos(1)+1)+(sin(1)+1)+\frac 1 5\] \[cos(1)sin(1)+\frac{11}{5}\]
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
oops sine of 0 is zero
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
you have an extra +1 in there  yep
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
cos(1)sin(1)+ 6/5
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
looks good to me :)
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.2
sigh...finally! Thanks guys!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
welcome !
 2 years ago
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