Line Integrals with respect to x or y // Vector Calculus

Описание: Previously in my Vector Calculus playlist (link below), we talked about the line integral along some field. In this video we are going to focus on line integrals with respect to just one of the variables, x or y. There are two pleasing interpretation of this. When our line integral is geometrically interpreted as the surface area above some planar curve beneath some function, then the line integral with respect to x or y can be interpreted as the projection of that surface onto either the xz or yz plane. Alternatively, if we are doing a Line Integral of a vector field along a curve, the line integrals with respect to dx or dy is just zeroing out the j hat or i hat components respectively. Indeed, the line integral of a vector field can be decomposed into the line integrals with repect to x and y respectively.

MY VECTOR CALCULUS PLAYLIST:
►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line Integra...  

0:00 Surface Area Interpretation
3:00 Formula 1
4:35 Field Interpretation
5:57 Formula 2
8:18 Example


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►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...  
►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  
►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...  
► CALCULUS II:    • Calculus II (Integration Methods, Series, ...  
►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...  
►DIFFERENTIAL EQUATIONS:    • How to solve ODEs with infinite series | I...  

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   • 5 Tips To Make Math Practice Problems Actu...  
►Cool Math Series:
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