Integration with a unit step function

[killerfish]

Hi,

i have a problem with integration a function with a unit step function.

Homework Statement

Given,

Refer to the image, i dun understand is that u(t) is equal to 1 from a definite integration from -$$\infty$$ to $$\infty$$ since u(t)=1 from -$$\infty$$ to 0 and u(t)=0 from 0 to $$\infty$$.


Thanks.

 

[Mark44]

Hi,

i have a problem with integration a function with a unit step function.

Homework Statement

Given,

View attachment 23734

Refer to the image, i dun understand is that u(t) is equal to 1 from a definite integration from -$$\infty$$ to $$\infty$$ since u(t)=1 from -$$\infty$$ to 0 and u(t)=0 from 0 to $$\infty$$
since u(t) = 0 for all t < 0.


Thanks.

Isn't it the other way around like in your drawing? I.e., that u(t) = 0 for t < 0 and u(t) = 1 for 0 <= t < infinity?

That means that
$$\int_{-\infty}^{\infty} g(t) u(t)dt = \int_0^{\infty} g(t) dt$$

 

[killerfish]

Isn't it the other way around like in your drawing? I.e., that u(t) = 0 for t < 0 and u(t) = 1 for 0 <= t < infinity?

That means that
$$\int_{-\infty}^{\infty} g(t) u(t)dt = \int_0^{\infty} g(t) dt$$

so if i have muliplication of few unit step function like in the image below,

am i right this way?

 

[vela]

Ayuh.