We will create a parallelogram that approximates it

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: s it. Once the parallelogram is created we can easily find the area of it using what we learned from chapter 10. Area of Parallelogram = We know the tangent plane approximates the surface well near . Two vectors that lie in the tangent plane are and . For our small parallelogram, our movement in the x and y direction is not one, but a small change of and . So our vectors that represent the sides of the parallelogram are: and Thus the Area of Parallelogram can be derived below: Thus And finally the Surface Area = Example: Find the surface area of the portion of the paraboloid lying above the xy-plane. We need to know the projection of the surface in the xy-plane: Let z = 0 to get the projection: We need our partials to plug into the formula: ( Notice the change of coordinates to polar to make the limits a lot easier to find ) Summary of Section 13.4 1 Setting up and Evaluating a double integral that represents the Surface Area of a given surface Section 13.5 Triple Integrals For now we will start with an integrand...
View Full Document

Ask a homework question - tutors are online