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How can I convolve the following $u(t+1)*u(-t)$ I know that convolution with $u(t)$ gives the integral of a function but what change occurs due to $u(-t)$?

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In general, convolution of a function $f(t)$ with $u(-t)$ results in a function $g(t)$ defined by the following integral:

$$g(t)=\int_{-\infty}^{\infty}f(\tau)u(\tau-t)d\tau=\int_{t}^{\infty}f(\tau)d\tau\tag{1}$$

In the given example, $f(t)=u(t+1)$, so you get

$$g(t)=\int_{t}^{\infty}u(\tau+1)d\tau=\int_{t+1}^{\infty}u(\tau)d\tau\tag{2}$$

I leave it up to you to figure out what the result of that integral is.

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