MATH 182A Lecture Notes - Lecture 14: Polar Coordinate System
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L = z b a px2 + y2d . 1 r = f ( ) compared to y = f (x) x = r cos( ) = f ( ) cos( ) = y = r sin( ) = f ( ) sin( ) = dx d dy d . = f ( ) sin( ) + f ( ) cos( ) x2 + y2 = ( r sin( ) + )2 sin2( ) + r2 cos2( ) + 2r d sin( ) + r cos( ))2 sin( ) cos( )+ sin( ) cos( ) dr d . L = z b a rr2 + ( dr d . Find the integral for the area in common between the two functions: r = 1 + cos( ) r = 1 cos( ) 0 (1 cos( ))2d r = 3 sin( ) If any errors are found, please contact me at alvin. lin. dev@gmail. com.