Thread: Integrals using step functions

I have the integral from 1 to 5 of [h(t-2) + h(t)]lnt dt

I broke this integral into integral from 1 to 5 of [h(t-2)ln t] + integral from 1 to 5 of [h(t) lnt]

but now I don't know how to actually use the step function to find the answer..

Originally Posted by CookieC

I have the integral from 1 to 5 of [h(t-2) + h(t)]lnt dt

I broke this integral into integral from 1 to 5 of [h(t-2)ln t] + integral from 1 to 5 of [h(t) lnt]

but now I don't know how to actually use the step function to find the answer..

Do you know the definition of the step function? If so, apply it to your problem ....

h(t - a) = 1 if t>= a and 0 if t<a ? but uumm how do i know what t is..? :S

Wait is it because its bewteen 1 to 5?? so if its in between there we can say it is equal to 1 and if it is not then it is equal to 0?

Actually I don't understand it..

I have h(t-2) = 1 when t>=2 and 0 when t < 2

With the integral from 1 to 5 of h(t-2)lnt do i do integral from 1 to 2 of lnt x 0 is equal to zero then plus integral from 2 to 5 of lnt x 1?

Originally Posted by CookieC

Actually I don't understand it..

I have h(t-2) = 1 when t>=2 and 0 when t < 2

With the integral from 1 to 5 of h(t-2)lnt do i do integral from 1 to 2 of lnt x 0 is equal to zero then plus integral from 2 to 5 of lnt x 1?

You will need to break up the interval of integration into subintervals and use the appropriate value of the step functions in each of those subintervals.