(a) If C is the line segment connecting the point (x₁, y₁) to the point (x₂, y₂), show that

∫_C x dy − y dx = x₁y₂ − x₂y₁

(b) If the vertices of a polygon, in counterclockwise order, are (x₁, y₁), (x₂, y₂), . . . , (x_n , y_n), show that the area of the polygon is

(c) Find the area of the pentagon with vertices (0, 0), (2, 1), (1, 3), (0, 2), and (−1, 1).

Transcribed Image Text:

A = [(x1y2 - x2yı) + (x2y3 - x3y2) + ... + (xp-1ya – X,ya-1) + (x,yı – xi ya)] %3D