Thanks ! -
D - 3
XXXXXXXXXXIntegrate
XXXXXXXXXXIntegrate
3. Integrate
4. ...

Question

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 Preview: D - 3 XXXXXXXXXXIntegrate  x2x2-1dx XXXXXXXXXXIntegrate   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). XXXXXXXXXXIntegrate 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 XXXXXXXXXXIntegrate  sin7x dxThis document was truncated here because it was created in the Evaluation Mode.

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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