Finding the volume of the tetrahedron using triple integrals. D is the tetrahedron bounded by the coordinate planes and the plane 3x+3y+z=3, then express the volume of D as a triple integral.

Hayley Bernard 2022-07-16 Answered
Finding the volume of the tetrahedron using triple integrals
D is the tetrahedron bounded by the coordinate planes and the plane 3 x + 3 y + z = 3, then express the volume of D as a triple integral.
My Try:
The z-limits are 0 z 3 3 x 3 y
If y is the limit on the xy- plane then z = 0 0 y 1 x.
Similarly, 0 x 3.
Finally, the integral will be 0 3 0 1 x 0 3 3 x 3 y d z   d y   d x
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Answers (1)

fairymischiefv9
Answered 2022-07-17 Author has 11 answers
Explanation:
It is correct for y and z bounds but for x we have
- y = z = 0 x = 1 0 x 1
and therefore V = 0 1 d x 0 1 x d y 0 3 3 x 3 y d z
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