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Calc5

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User Generated
Subject
Calculus
School
The University of Texas at El Paso
Type
Homework
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1.

 Substitute

 and the integral becomes

 
 
so the answer is D.
2.


 Integrate the first equality:

 
   
To determine use the second equality:
     
so 
     and the answer is C.
3.
  find the area under
and over the x-axis on

This area is the integral

because
is positive. The integral is the limit of sums


Here
  
(right endpoints) and 
Then
  
  
 
 
and the sum equals to
 




We know



  


  

  
so the initial sum is equal to
  
  
 
 
Obviously

and

 so the integral sum tends to    
 

i.e. the answer is B.

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1 1 1 1 1. ∫ 𝑥 2 cos (𝑥) 𝑑𝑥. Substitute 𝑢 = 𝑥 , 𝑑𝑢 = − 𝑥 2 𝑑𝑥 and the integral becomes 𝟏 ∫(− cos 𝑢)𝑑𝑢 = − sin 𝑢 + 𝐶 = − 𝐬𝐢𝐧 ( ) + 𝑪, 𝒙 so the answer is D. 2. 𝑦 ′ (𝑥) = 1 √𝑥+2 , 𝑦(2) = −1 . Integrate the first equality: 𝑦(𝑥) = ∫ 𝑑𝑥 = 2√𝑥 + 2 + 𝐶. √𝑥 + 2 To determine 𝐶, use the second equality: 𝑦(2) = 2√4 + 𝐶 = 4 + 𝐶 = −1, so 𝐶 = −5, 𝒚(𝒙) = 𝟐√𝒙 + 𝟐 − 𝟓 and the answer is C. 3. 𝑓(𝑥) = 𝑥 2 + 3, find the area under ? ...
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Anonymous
Really useful study material!

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