Lengths of Curves

1
Lengths of Curves

• 7.4

2
Distance Between Two Points
3
Arc Length

• If a smooth curve begins at (a,c) and ends at
  (b,d), altb, cltd, then the length of the curve is
• If y is a smooth function of x on a,b

4
Arc Length

• If a smooth curve begins at (a,c) and ends at
  (b,d), altb, cltd, then the length of the curve is
• If x is a smooth function of y on c,d

5
Smooth Curve

• If the function has a continuous first
  derivative, then the function is smooth and the
  graph will be a smooth curve.

6
Vertical Tangents, Corners, and Cusps

• At points where the derivative is undefined there
  are work-arounds.
• Work with ys instead of xs or vice versa.
• Example x(1/3) has a vertical tangent at x0,
  so use x y3 instead.
• Split up the integral so that the undefined
  points are now limits on the integral.
• See example 4 in the book.

7
Examples

• 4,8,14,18,28