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The line intergral is a super interesting topic from multivariable calculus. Its used to do physics, from: Work (W), to Amperes Law to Faradays law and so on. In this video Im going to give an introduction to the line integral focusing mainly on visual intuition rather than notation and formulas. A scalar field is essentially a function that takes in multiple inputs and spits out one output. For example lets look at the function: f(x,y)=x^2+y^2 This function takes in two inputs and gives one output. We can graph this function in the x-y and z plane (x,y,z) which look like this. Take a moment to look at certain points and the overall look of the graph I encourage you to try a few 3D plotters and play around with them. Try functions you know in 2D with a mix of x and y. (Ive left a few in the description below) Before I talk about a line intergral, I want to recap the concept of Arc Length from Calculus 2. Lets look at a continous differentiable function f(x). Lets take a st
