Approximation of Accumulative Physical Quantity

Similarly to the length of a function, physical quantity related to the length of function can also be determine by integration when the physical qunatity can be expressed as infinitesimal elements.

Perimeter of a Semicircle

The perimeter of a circle can be deterimine by intergration by calculating the curve length of a semicircle over the diameter of the circle.. For example, a semicircle y=(r2-x2)1/2 [-r,r]

Graphically,

The perimeter of a semicircle is