Line Integral of Clockwise Circle
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Considering the circle $x^2+y^2=9$ going in the clockwise direction, I am evaluating the line integral $int_{C}$ $Fdr$ from $(3,0)$ to $(0,3$). I have parametrization $x=3cost$ and $y=3sint$ and I had a question on the limits of integration, as it is 3/4 of a circle and traveling clockwise. I don't think it is from 0 to $pi$$/2$ considering the orientation. Any help is appreciated.
calculus integration line-integrals
asked Nov 23 at 21:44
darklord0530
613
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up vote
0
down vote
favorite
Considering the circle $x^2+y^2=9$ going in the clockwise direction, I am evaluating the line integral $int_{C}$ $Fdr$ from $(3,0)$ to $(0,3$). I have parametrization $x=3cost$ and $y=3sint$ and I had a question on the limits of integration, as it is 3/4 of a circle and traveling clockwise. I don't think it is from 0 to $pi$$/2$ considering the orientation. Any help is appreciated.
calculus integration line-integrals
asked Nov 23 at 21:44
darklord0530
613
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Considering the circle $x^2+y^2=9$ going in the clockwise direction, I am evaluating the line integral $int_{C}$ $Fdr$ from $(3,0)$ to $(0,3$). I have parametrization $x=3cost$ and $y=3sint$ and I had a question on the limits of integration, as it is 3/4 of a circle and traveling clockwise. I don't think it is from 0 to $pi$$/2$ considering the orientation. Any help is appreciated.
calculus integration line-integrals
asked Nov 23 at 21:44
darklord0530
613
Considering the circle $x^2+y^2=9$ going in the clockwise direction, I am evaluating the line integral $int_{C}$ $Fdr$ from $(3,0)$ to $(0,3$). I have parametrization $x=3cost$ and $y=3sint$ and I had a question on the limits of integration, as it is 3/4 of a circle and traveling clockwise. I don't think it is from 0 to $pi$$/2$ considering the orientation. Any help is appreciated.
calculus integration line-integrals
calculus integration line-integrals
asked Nov 23 at 21:44
darklord0530
613
asked Nov 23 at 21:44
darklord0530
613
asked Nov 23 at 21:44
darklord0530
613
asked Nov 23 at 21:44
darklord0530
613
asked Nov 23 at 21:44
darklord0530
613
613
add a comment |
add a comment |
3 Answers
3
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up vote
2
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accepted
Then your limits are $0$ and $-{3pi over 2}$ as following$$int_CFcdot rdthetahat a_theta=int_{0}^{-{3pi over 2}}3F_theta(r,theta) dtheta$$
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
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up vote
3
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Alternatively,
$$ int_C F ,mathrm dr = -int_{-C} F , mathrm dr, $$
where $-C$ is traversed in the anti-clockwise direction.
answered Nov 23 at 21:51
MisterRiemann
5,1981623
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up vote
2
down vote
For clockwise, you want $y = -3sin(t)$
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
Then your limits are $0$ and $-{3pi over 2}$ as following$$int_CFcdot rdthetahat a_theta=int_{0}^{-{3pi over 2}}3F_theta(r,theta) dtheta$$
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
add a comment |
up vote
2
down vote
accepted
Then your limits are $0$ and $-{3pi over 2}$ as following$$int_CFcdot rdthetahat a_theta=int_{0}^{-{3pi over 2}}3F_theta(r,theta) dtheta$$
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
Then your limits are $0$ and $-{3pi over 2}$ as following$$int_CFcdot rdthetahat a_theta=int_{0}^{-{3pi over 2}}3F_theta(r,theta) dtheta$$
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
Then your limits are $0$ and $-{3pi over 2}$ as following$$int_CFcdot rdthetahat a_theta=int_{0}^{-{3pi over 2}}3F_theta(r,theta) dtheta$$
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
answered Nov 23 at 21:50
Mostafa Ayaz
13.1k3735
13.1k3735
add a comment |
add a comment |
up vote
3
down vote
Alternatively,
$$ int_C F ,mathrm dr = -int_{-C} F , mathrm dr, $$
where $-C$ is traversed in the anti-clockwise direction.
answered Nov 23 at 21:51
MisterRiemann
5,1981623
add a comment |
up vote
3
down vote
Alternatively,
$$ int_C F ,mathrm dr = -int_{-C} F , mathrm dr, $$
where $-C$ is traversed in the anti-clockwise direction.
answered Nov 23 at 21:51
MisterRiemann
5,1981623
add a comment |
up vote
3
down vote
up vote
3
down vote
Alternatively,
$$ int_C F ,mathrm dr = -int_{-C} F , mathrm dr, $$
where $-C$ is traversed in the anti-clockwise direction.
answered Nov 23 at 21:51
MisterRiemann
5,1981623
Alternatively,
$$ int_C F ,mathrm dr = -int_{-C} F , mathrm dr, $$
where $-C$ is traversed in the anti-clockwise direction.
answered Nov 23 at 21:51
MisterRiemann
5,1981623
answered Nov 23 at 21:51
MisterRiemann
5,1981623
answered Nov 23 at 21:51
MisterRiemann
5,1981623
answered Nov 23 at 21:51
MisterRiemann
5,1981623
5,1981623
add a comment |
add a comment |
up vote
2
down vote
For clockwise, you want $y = -3sin(t)$
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
add a comment |
up vote
2
down vote
For clockwise, you want $y = -3sin(t)$
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
add a comment |
up vote
2
down vote
up vote
2
down vote
For clockwise, you want $y = -3sin(t)$
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
For clockwise, you want $y = -3sin(t)$
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
answered Nov 23 at 21:47
ncmathsadist
41.9k259101
41.9k259101
add a comment |
add a comment |
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