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1、Chapter 5 Applications of Definite Integrals,5.3 Lengths of Plane Curves,5.1 Volumes by Slicing and Rotation About an Axis,5.2 Modeling Volume Using Cylindrical Shells,5.4 Springs, Pumping and Lifting,5.5 Fluid Forces,5.6 Moments and Centers of Mass,5.3,Lengths of Plane Curves (平面曲线长度),A smooth curv
2、e （光滑曲线）,The function has continuous derivatives on the interval a,b.,5.3.1,Length of the curve of the Explicit Functions,Step 1. Subdivide the interval a,b into subintervals.,Step 2. Find a suitable approximation to any subinterval.,Step 3. Take the sum of above products.,Step 4. Take the limitation of Riemann sum.,Solution.,Solution.,Solution.,5.3.2,Length of the Parametrized curve,Supposed that a curve can be described by the parametric equations,Exercises,P420 3, 15, 16.,
