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Simply Sliced Sine (Posted on 2010-01-26) Difficulty: 2 of 5

∫ {sin {x}} dx

(i) {x}= x - [x], where, [x] is defined as the greatest integer ≤ x
(ii)The angles are in radians.

See The Solution Submitted by K Sengupta    
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Solution solution Comment 1 of 1
The argument to the sine function is always positive, from zero to one. The integral of that 1-unit-long segment of sine is (-cos(1) - (-cos(0))) = 1 - cos(1). This recurs in each of the six unit segments of x from -3 to +3, so the answer is 6(1 - cos(1)). Numerically this is approximately 2.758186164791162.
  Posted by Charlie on 2010-01-26 12:55:23
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