Question

Using direct integration, find [u(t)-u(t-1)] ∗ [u(t)-u[(t-2)].

Answer 1

To find [u(t)-u(t-1)] ∗ [u(t)-u[(t-2)] using direct integration, we integrate each part separately and then multiply the results together. The integral of [u(t)-u(t-1)] is 1 and the integral of [u(t)-u(t-2)] is 2. Multiplying these two results together gives us 2.

Step-by-step explanation:

To find the integral of [u(t)-u(t-1)] ∗ [u(t)-u[(t-2)] using direct integration, we can break it down into two parts: [u(t)-u(t-1)] and [u(t)-u(t-2)].

For the first part, [u(t)-u(t-1)], we integrate with respect to t from 0 to t:

∫[u(t)-u(t-1)] dt = t - (t-1) = 1

For the second part, [u(t)-u(t-2)], we integrate with respect to t from 0 to t:

∫[u(t)-u(t-2)] dt = t - (t-2) = 2

Multiplying the results of the two integrals together, we get:

1 * 2 = 2