Evaluate ∫ ∫ ∫ ( X + Y + Z ) D X D Y D Z Over the Tetrahedron Bounded by the Planes X = 0, Y = 0, Z = 0 and X + Y + Z = 1. - Applied Mathematics 2
Evaluate `int int int (x+y+z)` `dxdydz ` over the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and x + y + z = 1.
`I=int_(x=0)^1 int_(y=0)^(1-x) int_(z=0)^(1-x-y) (x+y+z)dzdydx`
`I= int_(x=0)^1 int_(y=0)^(1-x) [(x+y+z)^2/2]^(1-x-y) dydz`
`I=1/2 int_(x=0)^1 int_(y=0)^(1-x) [1-(x-y)^2]dydx`
`I=1/2 int_(x=0)^1 [y-(x+y)^2/2]^(1-x) dx`
`I= 1/2. 3/12=1/8`
Concept: Linear Differential Equation with Constant Coefficient‐ Complementary Function
Is there an error in this question or solution?
why create a profile on Shaalaa.com?
1. Inform you about time table of exam.
2. Inform you about new question papers.
3. New video tutorials information.