*This preview shows
pages
1–4. Sign up
to
view the full content.*

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **y = g ( t ), with x ( ) = a and x ( ) = b , then b a y dx = Example 2.1. (problem 31) Use the parametric equations of an ellipse, x = a cos , y = b sin , 2 , to Fnd the area that it encloses. 3. Lengths of Curves Recall we Fnd the length of a curve by b a 1 + dy dx 2 dx or d c 1 + dx dy 2 dy If x and y are parameterized by t as x = f ( t ) and y = g ( t ), with t , and the curve is traversed exactly once as t increases from to , then the length is given by Example 3.1. (problem 47) ind the length of the curve. x = e t-t , y = 4 e t/ 2 , and-8 t 3 . Section 10.2 Calculus with Parametric Curves 4 4. Surface Area Remark 4.1. ds = 1 + ( dy dx ) 2 dx = 1 + dx dy 2 dy = Example 4.1. (problem 60) Find the area of the surface obtained by rotating about the x-axis. x = 3 t-t 3 , y = 3 t 2 , and t 1 ....

View
Full
Document