Please showexplain your answer fx y zdV Evaluate the triple

Please show\\explain your answer

f{x, y, z)dV Evaluate the triple integral Q f(x, y, z) = 2xz + xy Q is the tetrahedron bounded by x + y + 2z = 2 and the coordinate planes. 2/3 2 4/15 1/5

Solution

f(x,y,z)= 2xz+ xy

x+y +2z= 2

y=0 and z=0 ==> x=2

0<x<2

z=0 ==> y= 2-x

0<y<2-x

2z= 2- x-y ==> z= (2- x-y)/2

0<z< (2- x-y)/2

\\int_{x=0}^{2} \\int_{y=0}^{2-x} \\int_{z=0}^{(2-x-y)/2} (2*x*z+x*y) dz dy dx

= 4/15 ANSWER