Use the given equations

$$

x$2$a$2$

$+$

y$2$b$2$

$=1,$ x $=$ au$,$ y $=$ bv

to find the volume of each dome$-$shaped solid lying below the surface z $=$ f$($x$,$ y$)$ and above the elliptical region R$.($Hint: After making the change of variables given by the equations, make a second change of variables to polar coordinates.$)$

$($a$)$

f$($x$,$ y$)=49$ x$2$ y$2$

R:$$

x$249$

$+$

y$236$

$1$

$($b$)$

f$($x$,$ y$)=$ A cos$$

$2$

x$2$a$2$

$+$

y$2$b$2$

R:$$

x$2$a$2$

$+$

y$2$b$2$

$1$