Chapter 3 - Triple Integrals

Question 1

Substitution in a triple integral

Answer 1

Triple integral over R of [g (x,y,z)dxdydz]

= triple integral over R’ of [g (F (u,v,w)) * |jacobian| ] dudvdw

Question 2

Volume of R

Answer 2

= triple integral of 1 dV

Question 3

Average of f over R
where f (x,y,z) is a smooth function drfined on a suitable region R

Answer 3

(Triple integral over R of f (x,y,z) dxdydz) / vol (R)