Evaluate:

5
∫ [|y-3| + [y]] dy
-1

Bonus Question:

Work out the following definite integral:

5
∫ (|y-3| + [y]) dy
-1

Notes:

(i) [x] is defined as the greatest integer ≤ x

(ii) |x| is the absolute value of x.

The easiest solution is to graph each function for the given integral (i.e. interval).  The first function is strictly a step function while the bonus function combines a step function and a ramp function.

The solutions are 16 and 19 respectively. 

Posted by hoodat on 2008-04-28 16:37:29