Answer:
The answer is A
Step-by-step explanation:
The rectangular has a height of 4 unit and has a width of 7 units. Area of the rectangular is:
28 unit square.
The point of (2,2) is on the middle height of rectangular shape. The point has 2 unit distance to base and ceiling of the rectangular.
The line y=2 is passing thought on (2,2) and also divides rectangular into two rectangular which have 14 unit square area.
Therefor, the slope is 0
For each <em>x</em> in the interval 0 ≤ <em>x</em> ≤ 5, the shell at that point has
• radius = 5 - <em>x</em>, which is the distance from <em>x</em> to <em>x</em> = 5
• height = <em>x</em> ² + 2
• thickness = d<em>x</em>
and hence contributes a volume of 2<em>π</em> (5 - <em>x</em>) (<em>x</em> ² + 2) d<em>x</em>.
Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:
