Answer
(a) 288
(b)144
Work Step by Step
First of all we should draw the region of rectangle in given conditions:
Given Region is :
R={(x,y)| 0<=x<=6, 0<=y<=4}
In part(a) we find change in x-axis and y-axis , after this we will find the value of change A. After we riemann sum and then we get volume of the solid 288 that lies below the surface z=xy and above the rectangle R={(x,y)| 0\leqx\leq6,0\leqy\leq4}
Note: for find the volume wwe use the points of upper right cornerof each square.
In part (b ) by using part (a) graph we estiate the mid-point in each rectangle , according to mid-points values ,put into riemann sum by Mid-points . in this case area will be remain same.
Plug all values in formula , we get the volume of the solid 144 [using part(a)].
