Thread: Shifted fcn...

Given:

x(t) = u(t) - u(t-10)

calculate:

Int(x^2)tdt


Am I thinking about this correctly... u(t) is 0 from neg. infinity to 0, and 1 after. u(t-10) is the same thing just shifted to the right to "turn on" at 10. So in effect we have a rectangle of amplitude 1 with bounds from 0 to 10. So our integral becomes:

int (1)^2 dt (with bounds of 0 and 10), which = 10?

your thinking won't be true in general (and we don't even have a definite integral here). Take , for instance. I think we need more info here, if you have some definite answer to get to, as opposed to an expression.

I'm assuming that is intended to notate the Heaviside step function, not an arbitrary function.

In any case, could you clarify whether this is a definite or indefinite integral? If we take it as written, it would be an indefinite integral, i.e.,



As you observed, you could define as a piecewise function like so:



Then we could find the anti-derivative using piecewise techniques.

If instead you are calculating a definite integral whose bounds cover the 0 to 10 range, then your work is correct.