High number_ Chapter 4__ curvilinear integral

Curve integral , Is to extend the concept of integral to a curve arc

One   Calculation of curve integral of arc length

Case one ,  x Parametric equation for parameters  ：

If the curve L It is given by rectangular coordinate equation , namely L:   y=y(x),     a≤x≤b , Then it can be transformed into x Parametric equation for parameters

(a ≤ x ≤ b),  thus  ,  therefore

The second case ,  Polar coordinate parameter equation ：

 

Look at an example ：