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  1. J

    Verify Greens theorem half done

    Homework Statement Verify Greens theorem for the line integral ∫c xydx + x^2 dy where C is the triangle with vertices (0,0) (1,1) (2,0). This means show both sides of the theorem are the same. Homework Equations ∫c <P,Q> dr = ∫∫dQ/dx -dP/dy dA ∫c xydx + x^2dy The Attempt at a...
  2. J

    Help solving line integral question

    hHomework Statement Evaluate ∫xy|dr| over the path given by x=t^3, y=t^2, t=0...2 Homework Equations x=t^3, y=t^2, t=0...2 The Attempt at a Solution x=t^3, y=t^2 y^(3/2) =x, y=t, x=t^(3/2), t=0...4 ∫0to4 t^5/2 [Sqrt((3t^(1/2))/2)^2 +(1)^2] =∫0to4 t^5/2 [Sqrt(9t/4 + 1) dt...
  3. J

    Finding Parametric equations for the line of intersection of two plane

    Homework Statement Find the parametric equations for the line of intersection of two planes Homework Equations Equations for the two planes... z=x+y,-------(1) 2x-5y-z=1 -----(2) The Attempt at a Solution My answers are not correct so I guess I'm going about it the wrong way. Someone...
  4. J

    Finding mass and center of mass of solid

    Homework Statement Find the mass and the center of mass of the solid E with the given density function ρ(x,y,z). E is bounded by the parabolic cylinder z = 1 – y2 and the planes x + 4z = 4, x=0, and z=0; ρ(x,y,z) =6. m=? x=? y=? z=? Homework Equations z = 1 – y2 and the planes x...
  5. J

    Finding the point of intersection between two curves. (Vectors)

    Homework Statement At what point do the curves r1(t) = (t, 4-t, 63+t^2) and r2(s)= (9-s, s-5, s^2) intersect? Answer in the form: (x,y,z) = ____ Find the angle of intersection theta to the nearest degree. Homework Equations The Attempt at a Solution i: t=9-s j: 4-t=s-5...