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Integration: finding equatin for y

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Pupil
Karma Points: 75
Respect (77%):
Date Posted: 7/24/2008 1:21:14 AM  Status: Closed
Integration: finding equatin for y
Course Textbook Chapter Problem
Calculus Calculus: Early Transcendental Functions (4th) by Edwards, Hostetler, Larson 5.1 56E
Question Details:
   Find the equation for y, given the derivative and the points on the curve.
=     Point(e,3)
 
This is what I have
y=3ln+c
3=3ln+c
=
c==1
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Answers:

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Mentor
Karma Points: 597
Date Posted: 7/24/2008 1:38:25 AM  Status: Live
Asker's Rating: Helpful   
Response:
dy/dx=3/x
y=Integrate[3/x,x]
y=3ln(x)+C
since y(e)=3
then 3=3+C
C=0
so the final equation becomes
y=3ln(X)
bye

 

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Guru
Karma Points: 1,730
(University of Kentucky)
Date Posted: 7/24/2008 1:38:57 AM  Status: Live
Asker's Rating: Lifesaver   
Response:
If  then    by the Fundamental Theorem of Calculus...
 
Therefore 
 
Now to find   we use the fact that   and therefore....
 
 
Therefore our function is     ANSWER
  
Hope this helps!
 
Jonathan
Jonathan Ross
University of Kentucky
B.A. Mathematical Economics

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Sage
Karma Points: 5,455
(Melbourne University)
Date Posted: 7/24/2008 1:43:41 AM  Status: Live
Asker's Rating: Helpful   
Response:
dy/dx=3/x

y=3ln(x)+C
..............................................>y(e)=3
then 3=3+C
C=0



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