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integral of modulus

Fermat

Active member
Nov 3, 2013
188
How would I compute the following integral? Let t be in [0,1].

$\int_{0}^{t}|s-t|\,ds$
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
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

Well-known member
MHB Math Helper
Jan 29, 2012
1,151
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]