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Empowered Integral (Posted on 2007-10-12) Difficulty: 2 of 5
Evaluate:

5
∫ 3{y} dy
0

where [p] is the greatest integer ≤ p, and {p} = p - [p]

See The Solution Submitted by K Sengupta    
Rating: 2.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 2 of 5 |

3^{y} is a sawtooth function, repeating every 1 unit change in y.

So Integral, 0 to 5, of 3^{y} dy is 5 * Integral, 0 to 1, of 3^y dy, as y={y} in that interval.

3^y = e^(y*ln(3))

so

Integral, 0 to 1, of 3^y dy = Integral, 0 to 1, of e^(y*ln(3)) dy = [(3^y) / ln3] evaluated from 0 to 1 = 3/ln3 - 1/ln3 = 2/ln3.

Five times that is 10/ln3 ~= 9.102392266268373

 


  Posted by Charlie on 2007-10-12 11:06:04
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