Computing the integral of |s-t| from 0 to t

Fermat1 · Dec 30, 2013

How would I compute the following integral? Let t be in [0,1].

$\int_{0}^{t}|s-t|\,ds$

alyafey22 · Dec 30, 2013

Fermat said:

How would I compute the following integral? Let t be in [0,1].

$\int_{0}^{t}|s-t|\,ds$

Since you are integrating on the interval $[0,t]$ so we have $0\leq s \leq t$.

HallsofIvy · Dec 30, 2013

Fermat said:

How would I compute the following integral? Let t be in [0,1].

$\int_{0}^{t}|s-t|\,ds$

The integral is for s from 0 to t so s is always less than t and s- t is always negative. |s- t|= -(s- t) so
[tex]\int_0^{t}|s- t| ds= -\int_0^t (t- s) ds= \left[ts- s^2/2\right]_0^t= t^2/2[/tex]

Computing the integral of |s-t| from 0 to t

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