$(a)Useanappropriate$ double integral $todetermine$ the area $ofanelement$ whose inner boundary,

$r1,and$ outer boundary, $r2,are$ given $inpolar$ coordinates $bythe$ formulas

$r1=A+$Bsin$(4),r2=C+$Bcos$(4)$

where $04.$

$Anexampleofthe$ element with $A=8,B=2,andC=12A,B,Cbefore$ evaluating your integral.$A=21$

$B=4$

$C=A+abs(B)+7$

Figure $Q2a$: Example image $ofthe$ element with $A=8,B=2,andC=12$

$(a)$ Use $an$ appropriate double integral $to$ determine the area $ofan$ element whose inner boundary,

$r_1,$ and outer boundary, $r_2,$ are given $in$ polar coordinates $by$ the formulas

$r_1=A+$Bsin$(4),r_2=C+$Bcos$(4)$

where $0\frac{}{4}.$

$An$ example $of$ the element with $A=8,B=2,$ and $C=12A,B,C$ before evaluating your integral.

$A=35$

$B=12$

$C=35+abs(12)+9$

Figure $Q2a$: Example image $of$ the element with $A=8,B=2,$ and $C=12$