perplexus.info :: Calculus : Empower And Reciprocate

Empower And Reciprocate (Posted on 2007-11-24)

g(y) is a continuous function satisfying g(5-y) + g(y) = 0 for 0 ≤ y ≤ 5.

Evaluate:

       ₅
     ∫(1+ 5^g(y))^-1 dy
      ⁰

Submitted by K Sengupta

Rating: 3.0000 (2 votes)

Solution: (Hide)

The required value of the definite integral is 2.5

EXPLANATION:

I = Integral(1 + 5^g(y))^-1 dy, y= 0 to 5
= Integral(1 + 5^g(5-y))^-1 dy, y= 0 to 5
= Integral(1 + 5^-g(y))^-1 dy, y= 0 to 5
= Integral(5^g(y))/(1 + 5^g(y)) dy, y= 0 to 5
= I
or, 2I = = Integral dy, y= 0 to 5
or, 2I= 5, giving:
I = 5/2 = 2.5

Thus, the required value of the definite integral is 2.5.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Answer	Praneeth	2007-11-26 07:36:22
re(5): Switching integral! - format only	brianjn	2007-11-26 03:38:36
re(4): Switching integral! - format only	Bractals	2007-11-25 13:35:39
re(3): Switching integral! - format only	brianjn	2007-11-25 06:37:42
re(2): Switching integral!	Chesca Ciprian	2007-11-25 06:23:51
re: Switching integral!	brianjn	2007-11-24 17:33:31
A different switch that also works	Larry	2007-11-24 15:35:22
Switching integral!	Chesca Ciprian	2007-11-24 13:29:38

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