I dont know how to set up the integral for z pls help | Mathematics | Page 1

wintry flax Oct 13, 2022, 2:51 AM

#

Find the mass of the triangular-shaped solid bounded by the planes z= 1 + x,
z= 1 −x, z= 0, and with 0 ≤y≤3. The density is δ= 10 −zg/cm^3 and x,y,z
are in cm.

ruby cloak Oct 13, 2022, 4:41 AM

#

it's the integral of delta on the region defined by
z =< 1+x
z =< 1-x
0 =< z
0 =< y =< 3

#

think about it geometrically and you'll understand the first two inequalities

wintry flax Oct 13, 2022, 4:42 AM

#

yea but how do i set up the integral with 2 upper bounds

ruby cloak Oct 13, 2022, 4:45 AM

#

they imply
z =< 1

#

so you just need to show that this system of inequalities is equivalent to
0 =< z =< 1
z-1 =< x =< 1-z
0 =< y =< 3

wintry flax Oct 13, 2022, 11:26 PM

#

ok thank you!

#I dont know how to set up the integral for z pls help