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

so, converting firstly the mixed fractions to improper fractions and then "adding".

h/o/e/s mad

step-by-step explanation:

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