Thanks !- D - 3 1. Integrate 2. Integrate 3. Integrate 4. Integrate 5.Evaluate...

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Thanks !-  D - 3 1.      Integrate    2.     Integrate 3.    Integrate   4.   Integrate 5.Evaluate (Show your work. No fnint.) 6.    Using Trig. Substitution,  Integrate 7.Integrate 8.Integrate 9.   I			Document Preview:				D - 3 1.      Integrate  x2x2-1dx                   2.     Integrate   5-x5+x          3.    Integrate  cosxsin2x+1dx           4.   Integrate   xsinx dx           5.   Evaluate   12x3lnxdx  (Show your work. No fnint.)            6.    Using Trig. Substitution,  Integrate1x24-x2dx              7.   Integrate2x3-4x2-15x+5x2-2x-8dx                    8.   Integratex-19x2-3x-10dx                9.   Integrate  2x2-5x+2x3+xdx                   Find    limx?0tanx-xx3           Using the Disk Method, find the volume of the solid generated by  revolving about the x – axis the region bounded by the curve      y=4x2+4 , the x- axis, and the lines x = 0 and x = 2. (Use the trigonometric substitution x = 2tan? in solving the problem).           12.      Integrate secx dx (Do it.Do not just write down the  formula).       Show that the rule for Integration By Parts corresponds to the  Product Rule for differentiation.        Integratecscx dx               Evaluate V =  p1e[x2-(lnx)2]dx                 16. Integrate  sin7x dx     This document was truncated here because it was created in the Evaluation Mode.	D - 3 1.      Integrate          2.     Integrate    3.    Integrate   4.   Integrate    5.   Evaluate     (Show your work. No fnint.) 6.    Using Trig. Substitution,  Integrate 7.   Integrate 8.   Integrate 9.   Integrate   10. Find     11. Using the Disk Method, find the volume of the solid generated by  revolving about the x – axis the region bounded by the curve   , the x- axis, and the lines x = 0 and x = 2. (Use the trigonometric substitution x = in solving the problem). 12.      Integrate  (Do it.Do not just write down the  formula). 13. Show that the rule for Integration By Parts corresponds to the  Product Rule for differentiation. 14.  15.   Evaluate V =        16. Integrate   17.   Find   18.  19. Evaluate   20.   Find

Robert · Accepted Answer

D - 3 
1. Integrate  ∫
  
    

=∫
      
    

=∫
     
    
  +∫
 
    

=∫   + ∫
 
    

= x + (1/2)*log|
   
   
  + c        (from formula of ∫
 
    
  )
    2.     Integrate   ∫√
   
   
 
    ∫√
   
   
dx = ∫ √
(   )(   )
(   )(   )
dx 
            =∫
   
√     
   
              =∫
 
√     
   - ∫
 
√     
   
        (putting 25-x2 = z2=>-2xdx=2zdz =>-xdx=zdz) 
                                 =5*     
 
 
 + ∫
 
 
         (using the formula for ∫
 
√     
  ) 
          =5*     
 
 
  + z +c 
          =5*     
 
 
 + √      + c  (since z=√     )
3.Integrate  ∫
    
√       

            ∫
    
√       
   
 =∫
   
 √    
           (putting sin2x +1 = z2 =>2sin x cos x dx = 2zdz =>cos x dx=    
√    
) 
  =∫
  
√    
 
 =log (z + √    ) + c 
 =log(√        + sin x) + c
4.   Integrate   ∫         
∫          
=x∫         - ∫ 
 
  
 ∫            
=-x cos x + ∫         
=-xcos x + sinx +c 
=sin x – x cos x + c
5.   Evaluate   ∫      
 
 
    (Show your work. No fnint.)
∫
  
     
 
 – ∫
  
 
  ]1
2 
  
     
 
 –
  
]1
2 
 4ln 2-
  
  

6.    Using Trig. Substitution,  Integrate∫
 
  √    

       ∫
 
  √    
   
 =   ∫
     
      √        
         (putting x=2sin  => dx=       d ) 
= ∫
  
      
 
=
 
 
∫            
= -
    
 

7.   Integrate∫
             
       

       
 = 2x +
       

       
 =
   
 +
   
 
x+5=A(x-2) + B(x-4) 
Solving by comparing coefiicients in the numerator, we get A=9/2,

Thanks ! - D - 3 XXXXXXXXXXIntegrate XXXXXXXXXXIntegrate 3. Integrate 4. Integrate 5.Evaluate (Show your work. No fnint.) 6. Using Trig. Substitution, Integrate 7.Integrate 8.Integrate 9. I Document...

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