Coulomb's law and Electric field intensity problem

[rizwanibn]

I am not getting the answer to this question as shown in the textbook.
Please help...!

My attempt is in the last attachment.

Thanks.!

 

[blue_leaf77]

Be carefull with the absolute sign in the inequality. $0.1 \leq |x| \leq 0.2 = (x\leq -0.1 \cup x\geq 0.1) \cap -0.2\leq x \leq 0.2$.

 

[rizwanibn]

New attachment

 

[rizwanibn]

New attachment

 

[blue_leaf77]

Yes, I think that should give you the correct answer.

 

[rizwanibn]

Is it addition of subtraction in between...?

 

[blue_leaf77]

On a second thought, I think your the integration volume should be eight small cubes of sides 0.1 at each corner of a large cube of sides 0.4. As illustration for x-y plane, see picture below. The intersection area in that picture actually forms four long bar of square cross section when put in a 3D coordinate. If you add the last region corresponding to the inequality for $z$, you should get 8 cubes as the integration volume.

 

[rizwanibn]

Thanks very much.
Got a very good understanding of it.
So all the cubes has a pair of opposite sign and they cancel out each other.

 

[blue_leaf77]

You have to do the calculation to see if that's true.