Example: Curvilinear integral of a vector field

Example: work to lift a body up to a certain height

There is a certain work W = m·g·h (g accelleration of gravity, g = 9,81 m/s²) necessary to lift a body with mass m in the gravity field of earth along a certain curve up to a height h. This work W is not dependent on the specific form of the curve. Hint: Lifting a body gives a negative work. If the body is falling down the sign of the work is positive. Task Change the height h and the shape of the curve by moving point A, B, C and D. Check if there is always the same work necessary to lift a body up to the height h. How does th work change if point D is on the x-axis or below?