Calculus -2H.W # 2IBP - means Integration By Part1. Use the disk method to find the volume of the...

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Calculus -2H.W # 2IBP - means Integration By Part1. Use the disk method to find the volume of the solid formed by revolvingthe region bounded by the graph of f(x) = and the x-axis (about the x-axis.2. Find the arc length of the graph of y =  on the interval [1, 7]3. Use the shell method to find the volume of the solid generated byrevolving the region bounded by the graphs of y = 0, x = 3 about the y-axis.4. Evaluate 5. Integrate 6. Use Integration by Part to evaluate7. Integrate  (IBP method).8. Integrate Evaluate  (No fnInt)10.A cable suspended between two poles takes the shape of a catenarywhose equation is given by Where  Find the length of the cable, if x and y are inmeters.

Robert · Accepted Answer

Solution 1: 
By disk method: 
Area of disk is: 
   ( ( ))

  ∫  (√    )
 

  ∫        

   [     ] 

Hence the volume is :         
Solution 2: 
Length of arc is: 
  ∫√(  (  ) )   
  
 
 
 
 
  
     
 
  
  ∫√(    
 
 )   
  ∫√
(   
 
 )
 
 

  ∫
√   
 
 
 
 

Let:  
  (   
 
 ) 
   
 
 
  
 

 

 
 

  ∫( 
 
 )
 

 
 
 
 
 
 

   
 
  
Replacing t back 
  [(   
 
 )
 
 
]

  (            )        
Hence the length of arc is 7.228 units 
Solution 3: 
Shell strip is: 
     ( )
Hence volume is:

Calculus -2 H.W # 2 IBP - means Integration By Part 1. Use the disk method to find the volume of the solid formed by revolving the region bounded by the graph of f(x) = and the x-axis (about the...

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