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:

 
        
             
        
        
        
Answer:
Step-by-step explanation:
Given
Length of curve

Length of curve is given by 
 over interval a to b
 over interval a to b
comparing two we get


integrating


Curve Passes through (1,2)


curve is 

 
        
             
        
        
        
Answer:
2x Y,
Step-by-step explanation: