# Example: Curvilinear integral of a vector field

- Author:
- Andreas Lindner

- Topic:
- Calculus, Integral Calculus

## 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?