Evaluating integral involving Heaviside function.

[SherlockOhms]

Homework Statement

Evaluate ∫ (t - 1)^2 U(t - 2)dt on the interval [0, 5]

Homework Equations

τ = 2, b = 5.
U(t - τ) = 0, t < τ and 1, t > τ.

The Attempt at a Solution

Decompose integral up into two parts [0, 2] and [2,5].
U(t - 2) will = 0 on the first interval as t < τ and it will = 1 on the second as t > τ. From there it's just a case of evaluating ∫(t - 1)^2 dt on [2,5].
Does this sound correct or have I gone wrong somewhere?
Thanks.

 

[jbunniii]

That approach looks fine to me.

 

[SherlockOhms]

Good stuff. Thanks.