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Equate The Integrals, Get Constant (Posted on 2007-10-24) Difficulty: 3 of 5
Determine the value of a constant C such that:

0pi/3(sin y/cos2y)dy = ∫0C(√(z+C) - √z)-1dz

Note: The range of the first integral reads 'pi/3'.

  Submitted by K Sengupta    
Rating: 2.5000 (2 votes)
Solution: (Hide)
C = 9/32

EXPLANATION:

Substituting t = sec y, we obtain dt = sec y .tan y.dy

Thus, the integral on the right is:
integral(dt), t = 1 to 2
= 2-1 = 1

Also, the integral on the left:
= integral (V(z+C) VC)-1.dz, z = 0 to C
= (1/C)* integral (V(z+C) + VC)-1.dz, z = 0 to C
= 4*(V2/3)*VC

Thus, 32*C/9 = 1, giving C = 9/32, so that:

The required value of C is 9/32.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Sorry is the same result......!Chesca Ciprian2007-10-25 15:36:44
Hmmm....Chesca Ciprian2007-10-25 15:34:10
full solutionDaniel2007-10-24 18:18:26
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