Answer:
2x
Step-by-step explanation:
It would be 2x because once you do all of your work it would be 2x
The answer is 44%.!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
the total charge is
![Q=24(1-\exp(-1))nC\approx15.171nC](https://tex.z-dn.net/?f=Q%3D24%281-%5Cexp%28-1%29%29nC%5Capprox15.171nC)
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
![Q=\int^{6}_{-6}2\exp\left(\frac{-|x|}{6}\right)dx](https://tex.z-dn.net/?f=Q%3D%5Cint%5E%7B6%7D_%7B-6%7D2%5Cexp%5Cleft%28%5Cfrac%7B-%7Cx%7C%7D%7B6%7D%5Cright%29dx)
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![Q=\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx+\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx](https://tex.z-dn.net/?f=Q%3D%5Cint%5E%7B0%7D_%7B-6%7D2%5Cexp%5Cleft%28%5Cfrac%7Bx%7D%7B6%7D%5Cright%29dx%2B%5Cint%5E%7B6%7D_%7B0%7D2%5Cexp%5Cleft%28%5Cfrac%7B-x%7D%7B6%7D%5Cright%29dx)
using the substitution x=-u in the first integral we get![\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx=-\int^{0}_{6}2\exp\left(\frac{-u}{6}\right)du=\int^{6}_{0}2\exp\left(\frac{-u}{6}\right)du](https://tex.z-dn.net/?f=%5Cint%5E%7B0%7D_%7B-6%7D2%5Cexp%5Cleft%28%5Cfrac%7Bx%7D%7B6%7D%5Cright%29dx%3D-%5Cint%5E%7B0%7D_%7B6%7D2%5Cexp%5Cleft%28%5Cfrac%7B-u%7D%7B6%7D%5Cright%29du%3D%5Cint%5E%7B6%7D_%7B0%7D2%5Cexp%5Cleft%28%5Cfrac%7B-u%7D%7B6%7D%5Cright%29du)
which is the same as the first integral. Thus, the total charge is given by
![Q=2\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx](https://tex.z-dn.net/?f=Q%3D2%5Cint%5E%7B6%7D_%7B0%7D2%5Cexp%5Cleft%28%5Cfrac%7B-x%7D%7B6%7D%5Cright%29dx)
integrating we get
The answer would be x=7.
I hope this helps!
Apologies for this being answered late.