$1.R$ bounded $by$ the graphs $of$ the equations $y=x^3,y=x+6$

and $2y+x=0.$ Then find its area.

$2.f(x)=\sqrt[\phantom{2}]{x}+1$ and $g(x)=x^2+1.$

$(a)$ Find the volume $of$ the solid generated when the region bounded $byf$ and $gis$

revolved about the line $y=-1.$ Draw the solid.

$(b)$ Find the volume $of$ the solid generated when the region bounded $byf$ and $gis$

revolved about the line $x=1$ and $we$ decide $to$ integrate with respect $tox.$ Draw the

solid.

$3.xy-$plane bounded $by$ the graphs $of$

$y=4$ and $y=x^2.$ Find the volume $of$ the solid $if$ every cross section $by$ a plane

perpendicular $to$ the $x-$axis $isan$ isosceles right triangle with the hypotenuse $on$ the $xy-$

plane. $In$ your solution, draw a picture $of$ the solid and then draw a picture $of$ the

representative cross section.