A12-cm-long thin rod has the nonuniform charge density λ(x)=(2.0 nc/cm)e−|x|/(6.0 cm), where x is measured from the center of the rod. what is the total charge on the rod? hint: this exercise requires an integration. think about how to handle the absolute value sign

the total charge is

Step-by-step explanation:

Since x is measured from the center, that means that x=0 is the center so the edges of the rod correspond to x=-6 and x=6. that meas that the total charge can be calculated as

separating the integral from -6 to 0 and from 0 to 6, taking into account that |x|=-x for x<0 and |x|=x for x >=0, we get

using the substitution x=-u in the first integral we get

which is the same as the first integral. Thus, the total charge is given by

integrating we get

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