Q$1$: Evaluate the following $($each $10$ marks$)$

Evaluate the double integral over the region $R$ that is bounded by the graphs $y=x^2$ and $y=x^3.$ Choose the most convenient order of integration.

$(2x+4y+1)dA$

Evaluate the given iterated integral by reversing the order of integration:

${\displaystyle \underset{0}{\overset{1}{}}}{\displaystyle \underset{2y}{\overset{2}{}}}{e}^{-\frac{y}{x}}dxdy$

Find the area of the surface bounded by the graphs by the graphs $y=x^2$ and $y=x^3.$ Choose the most convenient order of integration.

$1dA$

Find the center of mass of the lamina that has the given shape and density.

$x=0,x=4,y=0,y=3$;$(x,y)=xy$