Recent content by ashina14

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    Evaluate integral for surface of a paraboloid

    Sorry LCKurtz, I forgot to mention, it is a reply to Hallsofly, as they've assumed z=2 whereas the question states it is 1. In response to your question, I completely understand where I went wrong now, looked up the formula, followed Hallsofly's method and got the answer of (1/420) (125√5 - 1)...
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    Evaluate integral for surface of a paraboloid

    It's given that z = 1 though
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    Simplifying the Integral of a Piece of Helix Using Stokes' Theorem

    |...i...j...k...l |...Px...Py...Pz...| |x^2-yz..y^2-xz..z^2-xy| better version of product
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    Simplifying the Integral of a Piece of Helix Using Stokes' Theorem

    Yes they give the same two points. I don't need to explicitly use the points I feel though. Sorry for giving you a headache! Doing it your way is much shorter indeed but it's still giving me an answer of zero: Taking vector F = (x2 -yz) i + (y2 -xz) j + (z2 -xy) so, taking cross product...
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    Simplifying the Integral of a Piece of Helix Using Stokes' Theorem

    Although I see how it can be done with ∇×F⃗ , thanks!
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    Simplifying the Integral of a Piece of Helix Using Stokes' Theorem

    Yes but I still don't feel the need to utilize the given points. Here's a solution I've come up with Changing the integrand in terms of the angle @ through x=acos@; dx=-asin@d@, y=asin@; dy=acos@d@, z=h@/(2pi); dz=hd@/(2pi), get I [from @=0 to @=2pi]S[(a^2)cos^2@-ah@sin@/(2pi)]...
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    Evaluate integral for surface of a paraboloid

    Homework Statement Evaluate s∫∫ lxyzl dS, where S is part of the surface of paraboloid z = x2 + y2, lying below the plane z = 1Homework Equations The Attempt at a Solution since z=1 and x2+y2=z, therefore integral becomes 0∫^1 0∫^(1-x2) xyz dy dx which solves to 1/8. Apprently this is...
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    Simplifying the Integral of a Piece of Helix Using Stokes' Theorem

    yes apparently it's a misprint! indeed z = hϕ/2π. I don't know the significance of B being the curve at ϕ=2π though.
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    Simplifying the Integral of a Piece of Helix Using Stokes' Theorem

    Not sure how to go from there either, I am supposed to get a 0 in the end but am failing to do so. How could I do it with Stoke's thm instead?
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    Simplifying the Integral of a Piece of Helix Using Stokes' Theorem

    Homework Statement Evaluate the integral ∫ (x2 − yz) dx + (y2 − xz) dy + (z2 − xy) dz, C(A→B) where C(A → B) is a piece of the helix x = a cos φ, y = a sin φ, z = h φ, (0 ≤ φ ≤ 2π), 2π connecting the points A(a, 0, 0) and B(a, 0, h). Homework Equations [Hint: The problem could...
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    Verify whether the following points are optimal solutions to the LP?

    Homework Statement Points (4,4) and (2,0) Minimise 3x1+6x2 s.t. 6x1-3x2=12 x1,x2>=0 Homework Equations The Attempt at a Solution I tried solving this the way LP questions are solved in general, graphically. So I drew a graph plotting the objective and the constraint...
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    Given a subspace S<=V, prove that there exists T<=V such that V=S⊕T.

    Thanks for the help anyway :)
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    Proving the Direct Sum Decomposition of a Vector Space

    Thanks for the help guys :)
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    Given a subspace S<=V, prove that there exists T<=V such that V=S⊕T.

    I didn't ask for a complete solution, I'm genuinely stuck. I'm not that acquainted with the unusual rules here as I don't come here often. Each of your warning is about a separate issue and I don't repeat the same mistake again. I would appreciate if you understand my position.
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    Given a subspace S<=V, prove that there exists T<=V such that V=S⊕T.

    How do I prove that? I don't see an obvious connection here