Use the shell method to compute the volume of the solids obtained by rotating the region enclosed by the graphs of the functions y=x2 and y=8−x2 for x≥0.5 about the y-axis.

44.18 cubic unit

Step-by-step explanation:

The intersection of the curve and is

Since we are rotating the region where we will use the intersection x = 2 and y = 4

Using the shell method with x ranges from 0.5 to 2. The volume of the shell would be

where h is the difference between the y-coordinates of the curves, in other words

Plug h into the V integral and we have

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870