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Getting Natural With Pi (Posted on 2007-11-27) Difficulty: 3 of 5
Determine the value of the constant y, whenever:
       y
     (ex - 1)-0.5 dx = pi/6 
      ln(4/3)

where ln x denotes the natural logarithm of x.

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Solution Switch to other integral! | Comment 3 of 8 |

Hi!

I found the same result y=ln(2) by switching to other integral like this:

x=ln(t^2+1)

So dx=2*t/(t^2+1)dt

and x1=ln(4/3) => t1=1/sqrt(3)

      x2=y => t2=sqrt(e^y-1)

The new integral is 2arctan(t) from t1 to t2.

After some calculus i receive y=ln(2)

 


  Posted by Chesca Ciprian on 2007-11-27 14:34:19
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