Integrate cos x cos y over the rectangle [0,pi/2] × [pi/2,pi]. We got -1 when we did this in class.

Integrate[ Cos[x]*Cos[y], {x,0,Pi/2}, {y,Pi/2,Pi}]

Check the 3-variable bowl volume we did in class (volume between x^2+y^2 and 2 over the region -1 ≤ x ≤ 1, -1 ≤ y ≤ 1). We got 16/3 in class.

Integrate[ 1, {x,-1,1},{y,-1,1}, {z,x^2+y^2,2}]

Integrate xy + yz over the tetrahedron from class. We got 1/60 in class.

Integrate[ x*y+y*z, {x,0,1},{y,0,1-x},{z,0,1-x-y}]