two integrals: int_M xy d(x,y) for M = {(x,y) : x,y >= 0, x + y <= 1}; and int_M ...

[lisahorkis]

two integrals: int_M xy d(x,y) for M = {(x,y) : x,y >= 0, x + y <= 1}; and int_M ...

hi,
i just found this forum. not sure if its the right section but i would appreciate your help on the following two integrals.

\(\displaystyle \displaystyle \int_M\, xy\, d(x,y),\, M\, =\, \{(x,\, y)\, \in\, \mathbb{R}^2\, :\, x,\, y\, \geq\, 0,\, x\, +\, y\, \leq\, 1\}\)

my answer: =1/24

\(\displaystyle \displaystyle \int_Z\, x\, e^y\, z^2\, d(x, y, z),\, Z\, =\, \{(x,\, y,\, z)\, \in\, \mathbb{R}^3\, :\, x^2\, +\, y^2\, \leq\, 1,\, -h\, \leq\, z\, \leq\, h\}\)

my answer: =0

are my solutions correct? i am really unsure about the 2nd one.

thanks!