Calculus 311–315

311.Substitutions in Triple Integrals
-General case
-Cylindrical Coordinates
-Spherical coordinates
-Example

312. Line Integral
-Definition
-Idea
-How to evaluate a line integral
-Example

313. Additivity
If a piecewise smooth curve C is made by joining a finite number of smooth curves end to end, then the integral of a function over C is the sum of the integrals over the curves that make it up.

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There is a note and example in the end of this part.

314. Mass and Moment Calculations
Here are the mass and moment formulas for coil springs, wires, and then rods lying along a smooth curve C in space:

-Mass
-First moments about the coordinate planes
-Coordinates of the center of mass
-Moments of inertia about axes and other lines

There is an example in the end of this part.

315. Line Integrals in the Plane
There are the idea and explanation about the line integrals in the plane.

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