PROPOSITION RESPECT! .HO ATTUAtTIOJf. 



II find th- -M of n uniform lamina in the form 



In situated in a sirai-ht line drawn 

 tlir.-u -!i the centre of t 'it angles to it* plane. 



>th and breadth of the rectangle. 



We hare t<> ral into two parts. For one 



part we integrate with respect to r from r-0 to r - a ace 0, 



and th.-n with respect to from 0-0 to 0-tan' 1 -. 



ther part we integrate with respect to r from r-0 

 to r &COSCC0, and tin n with respect to from 0tan~ 1 



to 0r "W multiply the result by 4. 

 ** rdr m \ 



(7T^" 



Integrate with respect to 0; thus we get 

 1 , csin0 



^rnte with respect to 6\ thus we get 



01, CCOS0 



he ix-'iuiivd r.-.-ult is 



x - ""' 



+ O) \( a +O 



' I 008 " *+*)*(?+* - >in " Vv'+lfvy-t" 



I 

 or 4/4 sin"* 



