ionic kettle
I've got the triple integral, which is bound by the axes & the function x/7+y/6+z/9=1. How can I determine where to stop in the integrals? Do I set the unknown to be equal to two variables when I am done integrating each iteration? We've only done with functions of 2 variables for the boundaries before, not 3.
echo light
everything (integrand, boundary functions) is smooth so basically all you need to do is to rewrite the system of inequalities as an equivalent one that isolate the variables the way you want to integrate
I would do the following:
The original system of inequalities (defining the region R) is
0 =< x, y, z
x/7 + y/6 + z/9 =< 1
This is equivalent to
0 =< y =< 6
0 =< x =< 1 - y/6
0 =< z =< 1 - y/6 - x/7
so you can integrate first in z, then in x and then in y using those boundaries
ionic kettle
That makes sense. Also got some help & did it with collapsing I think it’s called 🙂
echo light
collapsing? never heard of this...