Find the volume obtained when the shaded region is rotated
through 360' about the y-axis.​

Using the shell method, the volume is given by

That is, each cylindrical shell with radius x from the axis of revolution has height equal to the vertical distance between the upper curve (y = 2) and the lower curve (y = x ² + 1). Then the area of this shell is 2πrh = 2π x (2 - (x ² + 1)).

Computing the integral gives the volume,

i got 10.28 but that rounds up to 10.3

$650 per month plus utilities

step-by-step explanation:

just based on the info you gave, it would seem more cost effective to rent at $650 per month plus utilities.   if utilities are, in fact, $150 per month, your monthly living costs would be $800 as opposed to the other option of $825.