Vector calculus help please!?

Suppose a body of mass m is acted on by a constant planar force of the form f = (mg,0). Use the work formula ∫C f .dr


to find the work done in moving the body along the ellipical path C defined by ∫0Π/2 √(a2 sin2 t + b2 cos2 t) dt. What physical process might your results describe?

Vector calculus help please!?
I don't totally understand your question, so my apology if I answering something else.





First I will assume the path you want is the ellipse x^2/a + y^2 /b = 1, in a positive direction around the first quadrant.





Then the path is %26lt;a cost, bsin t %26gt;


the force field is %26lt;mg , 0 %26gt;





So multiply these togther and integrate :





∫mg a sin(t) over (0, pi/2)





= amg





Which would make sense, as we have moved a mass M, a distance of A, against gravity. (around a elliptical path)