Evaluate:

 3
∫ {sin {x}} dx
-3

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

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