- #1
Cloudless
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1. Evaluate the integral
∫VxdV
inside domain V, where V is bounded by the planes x=0, y=x, z=0, and the surface x2+y2+z2=1
Answer given: 1/8 - √2/16 (which is NOT what I got.. :yuck:)
2. The attempt at a solution
Ok, it's a triple integral, I know this.
∫dx runs from 0 to 1
∫dy runs from -√1-x2 to x
∫dz runs from 0 to √1-x2-y2
So the order of integrals go ∫∫∫dz dy dx
Yeah... it's not working. I keep getting stuck with things like x(1-y2-x2)1/2 which I can't integrate onwards...
∫VxdV
inside domain V, where V is bounded by the planes x=0, y=x, z=0, and the surface x2+y2+z2=1
Answer given: 1/8 - √2/16 (which is NOT what I got.. :yuck:)
2. The attempt at a solution
Ok, it's a triple integral, I know this.
∫dx runs from 0 to 1
∫dy runs from -√1-x2 to x
∫dz runs from 0 to √1-x2-y2
So the order of integrals go ∫∫∫dz dy dx
Yeah... it's not working. I keep getting stuck with things like x(1-y2-x2)1/2 which I can't integrate onwards...