University:
University of Central Florida
Course:
MAC 2312 | Calculus with Analytic Geometry II
Academic year:

2023
Views:

404

Pages:

3
Author:

Maria

2.4. Arc Length y=f(x) S = (x)²+(y)² 2 2 1 1 SSiCAx)²+ (Ay) 1:1 2 +13 a b Lim Ay lim f(x+ht f(x) Slim 1+ (0) Ax Ay12 + ho th dx a 3 y = 2x12 on 0 ≤ x ≤1 Ex: Find the length of y = b S = √(4) dx 12 dx = 1/1+(3x2) = √l+gx 1 S=√1+9x dx G 1 9√1+ 9x dx u=1+9x du 9 dx 0 10 27 10 Ex: Find the length of y=x²-lux for 1≤x≤3 2 8 dy=2x- dx 48 1 (4)²= (2x-x)² = 4x² + 4x2 ½ 2 2 1 olx 2 2=4x²+ olx 64x2 t 4x 2 3 4x²+1 3 1 S= 64x² + ½ dx 2 = 2x + dx = x² 13 3 8x =(3² + (131) - (12+111) = 8 +43 8 = 2x+ 8x 1 For x = f(y) → S =√1 + (dy 12 Ex: Find the length of x = 3y² between (3, 1) and (12,2) d (3,1) (12,2) dx = by dy 1+()=1+36y2 dy