$1).$Let $R=[2,6][-3,4].$ You can compute ${}_{R}6dA$ by interpreting the double integral as the volume of a rectangular solid, whose height is

$,$ whose width is $,$ and whose length is $$

So$,{}_{R}6dA=$

$2).$Consider the function $f(x,y)=6x^2-y$ over the rectangular region $R=[0,4][0,3].$

Divide the region $R$ into four equal rectangles. Then $x=$ and $y=.$

The upper right hand corners of these four rectangles are the points

$,,,$ and $$

Approximate the volume between $f(x,y)=6x^2-y$ and the $xy-$plane over the region $R,$ using the upper right hand corners of your rectangles:

${\displaystyle \underset{i=1}{\overset{2}{}}}{\displaystyle \underset{j=1}{\overset{2}{}}}f(x_i,y_j)xy=$

$$