Let F be the radial force field F = xI + yJ. Find the work done by this force along the following two curves, both which go from (0, 0) to (3, 9). (Use the Fundamental Theorem for Line Integrals instead of computing the line integral from the definition, as you did in the previous set. This way shows why the answers to the two parts must be the same - independence of path!)

A. If C1 is the parabola: x = t, y = t^2, 0 ≤ t ≤ 3, then ∫C1 F · dX = ???

B. If C2 is the straight line segment: x = 3t^2, y = 9t^2, 0 ≤ t ≤ 1, then ∫C2 F · dX = ???

Question

Let F be the radial force field F = xI + yJ. Find the work done by this force along the following two curves, both which go from (0, 0) to (3, 9). (Use the Fundamental Theorem for Line Integrals instead of computing the line integral from the definition, as you did in the previous set. This way shows why the answers to the two parts must be the same - independence of path!)

A. If C1 is the parabola: x = t,  y = t^2,  0 ≤ t ≤ 3, then ∫C1 F · dX = ???

B. If C2 is the straight line segment: x = 3t^2,  y = 9t^2,  0 ≤ t ≤ 1, then ∫C2 F · dX = ???

amistre64 · Answer

let r= r' = $$\int_{a}^{b}F(r(t))\cdot r'(t)~dt$$