Calculate the line integration of the vector field
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Calculate the line integration of the vector field

Calculate the line integration of the vector field

[From: ] [author: ] [Date: 11-05-09] [Hit: ]
......
Calculate the line integration of the vector field F= (x+y)i+(x^2+y^2)j along the unit circle clockwise.

-
Using x = cos t, y = -sin t for t in [0, 2π] for clockwise orientation:
∫c · dr
= ∫(t = 0 to 2π) · <-sin t, -cos t> dt
= ∫(t = 0 to 2π) (-sin t cos t + sin^2(t) - cos t) dt
= ∫(t = 0 to 2π) (-sin t cos t + (1/2)(1 - cos(2t)) - cos t) dt
= [-sin^2(t)/2 + (1/2)(t - sin(2t)/2) - sin t] {for t = 0 to 2π}
= π.

I hope this helps!
1
keywords: Calculate,the,vector,line,field,integration,of,Calculate the line integration of the vector field
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .