The line integral ∫(2y + 3z) dx + (x + 2z) dy + (y + x) dz was created using the combination p = 3, q = 2, and r = 3. This line integral can be used to calculate the area of the pentagon with vertices (2, 0, 0), (3, 4, 0), (3, 4, 5), (2, 0, 5), and (2, 0, 0).
These combinations of p, q, and r can be used to create the following line integrals:
∫(4y + 5z) dx + (3x + 4z) dy + (2x + 3y) dz
∫(3y + 4z) dx + (2x + 3z) dy + (x + 2y) dz
∫(2y + 3z) dx + (x + 2z) dy + (y + x) dz
The line integral ∫(4y + 5z) dx + (3x + 4z) dy + (2x + 3y) dz was created using the combination p = 1, q = 4, and r = 5. This line integral can be used to calculate the area of the triangle with vertices (2, 0, 0), (3, 4, 0), and (3, 4, 5).
The line integral ∫(3y + 4z) dx + (2x + 3z) dy + (x + 2y) dz was created using the combination p = 2, q = 3, and r = 4. This line integral can be used to calculate the area of the quadrilateral with vertices (2, 0, 0), (3, 4, 0), (3, 4, 5), and (2, 0, 5).
The line integral ∫(2y + 3z) dx + (x + 2z) dy + (y + x) dz was created using the combination p = 3, q = 2, and r = 3. This line integral can be used to calculate the area of the pentagon with vertices (2, 0, 0), (3, 4, 0), (3, 4, 5), (2, 0, 5), and (2, 0, 0).
Question
Calculus 3: Line Integrals (18 of 44) What is a Line Integral? [(y)dx+(z)dy+(x)dz] Example 6 and found that the different combinations of p and q that were given in the video that can be used to reverse engineer area into a line integral are:
p = 1, q = 4, r = 5
p = 2, q = 3, r = 4
p = 3, q = 2, r = 3