Line Integrals in the Plane

Line integrals in the plane provide a method for evaluating quantities distributed along a curve, such as mass, work, or surface area. A curve C in the plane is commonly represented parametrically by x = x(t) and y = y(t), where the parameter t varies over an interval [a, b]. ...

A mural is planned for the curved outer wall of a clock monument. To find the space available for the artwork, the total surface area of the curved wall must be found.

The base of the wall follows a curved path, C. This curve is defined by parametric equations, where x and y depend on the parameter t. As t