A Question on Density Tensors in General Relativity

[diaoye]

Homework Statement

this is a problem of exercise of general relativity by Gerard t Hooft

Problem 7, Transformation rule of a density
http://p13.freep.cn/p.aspx?u=v20_p13_photo_1211140612144629_0.jpg

sry i don't know how to type tensors with upper and lower indices. I can only show it by picture

Homework Equations

questions are in the picture

The Attempt at a Solution

I tried to read Geroch's "Geometrical Quantum Mechanics", (III Quantum Mechanics 14. Densities. Integrals. 15. States), but i still cannot understand it

 

[diaoye]

was i in a wrong section that nobody could help?