Line integral of a vector field along a curve C with two segments
Multi tool use
up vote
0
down vote
favorite
Vector field $ vec F = (3x^2y^3+8x)vec i + 3x^3y^2vec j$, along a curve C consisting of two segments C$_1$ and C$_2$.
Line segment C$_1$ given by $y = 0$ and $0 ≤ x ≤ x_0$ and the line segment C$_2$ given by $x = x_0$ and $0 ≤ y ≤ y_0$.
I need help calculating the line integral of:
$V(x_0,y_0) = int_0vec F cdot dvec r = int_C ((3x^2y^3+8x)dx + 3x^3y^2dy) $
The boundaries in the segments really throw me off, any help would be very much appreciated.
Thank you very much!
multivariable-calculus vectors vector-analysis vector-fields line-integrals
asked Nov 20 at 20:03
Fleuryette
11
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
Vector field $ vec F = (3x^2y^3+8x)vec i + 3x^3y^2vec j$, along a curve C consisting of two segments C$_1$ and C$_2$.
Line segment C$_1$ given by $y = 0$ and $0 ≤ x ≤ x_0$ and the line segment C$_2$ given by $x = x_0$ and $0 ≤ y ≤ y_0$.
I need help calculating the line integral of:
$V(x_0,y_0) = int_0vec F cdot dvec r = int_C ((3x^2y^3+8x)dx + 3x^3y^2dy) $
The boundaries in the segments really throw me off, any help would be very much appreciated.
Thank you very much!
multivariable-calculus vectors vector-analysis vector-fields line-integrals
asked Nov 20 at 20:03
Fleuryette
11
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 at 23:42
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Vector field $ vec F = (3x^2y^3+8x)vec i + 3x^3y^2vec j$, along a curve C consisting of two segments C$_1$ and C$_2$.
Line segment C$_1$ given by $y = 0$ and $0 ≤ x ≤ x_0$ and the line segment C$_2$ given by $x = x_0$ and $0 ≤ y ≤ y_0$.
I need help calculating the line integral of:
$V(x_0,y_0) = int_0vec F cdot dvec r = int_C ((3x^2y^3+8x)dx + 3x^3y^2dy) $
The boundaries in the segments really throw me off, any help would be very much appreciated.
Thank you very much!
multivariable-calculus vectors vector-analysis vector-fields line-integrals
asked Nov 20 at 20:03
Fleuryette
11
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Vector field $ vec F = (3x^2y^3+8x)vec i + 3x^3y^2vec j$, along a curve C consisting of two segments C$_1$ and C$_2$.
Line segment C$_1$ given by $y = 0$ and $0 ≤ x ≤ x_0$ and the line segment C$_2$ given by $x = x_0$ and $0 ≤ y ≤ y_0$.
I need help calculating the line integral of:
$V(x_0,y_0) = int_0vec F cdot dvec r = int_C ((3x^2y^3+8x)dx + 3x^3y^2dy) $
The boundaries in the segments really throw me off, any help would be very much appreciated.
Thank you very much!
multivariable-calculus vectors vector-analysis vector-fields line-integrals
multivariable-calculus vectors vector-analysis vector-fields line-integrals
asked Nov 20 at 20:03
Fleuryette
11
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 20:03
Fleuryette
11
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 20:03
Fleuryette
11
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 20 at 20:03
Fleuryette
11
asked Nov 20 at 20:03
Fleuryette
11
11
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Fleuryette is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 at 23:42
add a comment |
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 at 23:42
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 at 23:42
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 at 23:42
add a comment |
1 Answer
1
active
oldest
votes
up vote
0
down vote
hint
along $C_1 , dy=0$ gives
$$I_1=8int_0^{x_0}xdx=4x_0^2$$
along $C_2, dx=0$ and
$$I_2=3x_0^3int_0^{y_0}y^2dy=x_0^3y_0^3$$
the result is $$I=I_1+I_2$$
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
hint
along $C_1 , dy=0$ gives
$$I_1=8int_0^{x_0}xdx=4x_0^2$$
along $C_2, dx=0$ and
$$I_2=3x_0^3int_0^{y_0}y^2dy=x_0^3y_0^3$$
the result is $$I=I_1+I_2$$
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
add a comment |
up vote
0
down vote
hint
along $C_1 , dy=0$ gives
$$I_1=8int_0^{x_0}xdx=4x_0^2$$
along $C_2, dx=0$ and
$$I_2=3x_0^3int_0^{y_0}y^2dy=x_0^3y_0^3$$
the result is $$I=I_1+I_2$$
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
add a comment |
up vote
0
down vote
up vote
0
down vote
hint
along $C_1 , dy=0$ gives
$$I_1=8int_0^{x_0}xdx=4x_0^2$$
along $C_2, dx=0$ and
$$I_2=3x_0^3int_0^{y_0}y^2dy=x_0^3y_0^3$$
the result is $$I=I_1+I_2$$
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
hint
along $C_1 , dy=0$ gives
$$I_1=8int_0^{x_0}xdx=4x_0^2$$
along $C_2, dx=0$ and
$$I_2=3x_0^3int_0^{y_0}y^2dy=x_0^3y_0^3$$
the result is $$I=I_1+I_2$$
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
edited Nov 20 at 20:13
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
answered Nov 20 at 20:08
hamam_Abdallah
36.7k21533
36.7k21533
add a comment |
add a comment |
Fleuryette is a new contributor. Be nice, and check out our Code of Conduct.
Fleuryette is a new contributor. Be nice, and check out our Code of Conduct.
Fleuryette is a new contributor. Be nice, and check out our Code of Conduct.
Fleuryette is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3006814%2fline-integral-of-a-vector-field-along-a-curve-c-with-two-segments%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
KLdk ai0BCJ Qy,HVeDba1QRxq occI9i N5 YhWuESXeAi0dtAEb,3Bvfkyr1sPRk,djygBHQtD1DpJxzJtWCxNSQtXW AxUXmw
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 at 23:42