Mixing
Line integral of a vector field along a curve C with two segments
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 '18 at 20:03
Fleuryette
11
add a comment |
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 '18 at 20:03
Fleuryette
11
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 '18 at 23:42
add a comment |
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 '18 at 20:03
Fleuryette
11
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 '18 at 20:03
Fleuryette
11
asked Nov 20 '18 at 20:03
Fleuryette
11
asked Nov 20 '18 at 20:03
Fleuryette
11
asked Nov 20 '18 at 20:03
Fleuryette
11
asked Nov 20 '18 at 20:03
Fleuryette
11
11
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 '18 at 23:42
add a comment |
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 '18 at 23:42
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 '18 at 23:42
Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 '18 at 23:42
add a comment |
1 Answer
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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 '18 at 20:08
hamam_Abdallah
37.9k21634
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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 '18 at 20:08
hamam_Abdallah
37.9k21634
add a comment |
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 '18 at 20:08
hamam_Abdallah
37.9k21634
add a comment |
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 '18 at 20:08
hamam_Abdallah
37.9k21634
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 '18 at 20:08
hamam_Abdallah
37.9k21634
edited Nov 20 '18 at 20:13
answered Nov 20 '18 at 20:08
hamam_Abdallah
37.9k21634
answered Nov 20 '18 at 20:08
hamam_Abdallah
37.9k21634
answered Nov 20 '18 at 20:08
hamam_Abdallah
37.9k21634
37.9k21634
add a comment |
add a comment |
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Try visualizing this path: the first segment is horizontal, the second vertical.
– amd
Nov 20 '18 at 23:42