Please solve the screenshot! In this educational exercise, we explore line integrals and the computation of areas of polygons.**(a)** If \( C \) is the line segment connecting the point \( (x_1, y_1) \) to the point \( (x_2, y_2) \), calculate the following integral:\[\int_{C} x \, dy - y \, dx\]**(b)** Determine the area of a polygon with vertices in counterclockwise order, given as \( (x_1, y_1), (x_2, y_2), \ldots, (x_n, y_n) \). Select the correct formula:- \(\displaystyle A = \frac{1}{2} \left[ \left( x_1 y_2 - x_2 y_1 \right) + \left( x_2 y_3 - x_3 y_2 \right) + \cdots + \left( x_n y_1 - x_1 y_n \right) \right] \)- \(\displaystyle A = \frac{1}{2} \left[ \left( x_1 y_2 - x_2 y_1 \right) + \left( x_2 y_3 - x_3 y_2 \right) + \cdots + \left( x_{n-1} y_n - x_n y_{n-1} \right) + \left( x_1 y_n - x_n y_1 \right) \right] \)- \(\displaystyle A = \frac{1}{2} \left[ \left( x_2 y_1 - x_1 y_2 \right) + \left( x_3 y_2 - x_2 y_3 \right) + \cdots + \left( x_n y_{n-1} - x_{n-1} y_n \right) + \left( x_1 y_1 - x_n y_1 \right) \right] \)- \(\displaystyle A = \frac{1}{2} \left[ \left( x_1 y_2 + x_2 y_3 - x_3 y_2 \right) - \cdots - \left( x_n - 1 y_n - x_ny_n -

Name: Please solve the screenshot! In this educational exercise, we explore
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: Please solve the screenshot! In this educational exercise, we explore line integrals and the computation of areas of polygons.**(a)** If \( C \) is the line segment connecting the point \( (x_1, y_1) \) to the point \( (x_2, y_2) \), calculate the fo