Find the length of the curve
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Find the length of the curve

Find the length of the curve

[From: ] [author: ] [Date: 11-05-09] [Hit: ]
x^3/3 + x |(0,I hope this helps!-The arclength of some curve y =f(x) on the interval [a,= ∫(x² + 1) dx from 0 to 3 = x^3/3 + x eval.......
(1/3)(x^2+2)^1.5 from x=0 to x=3

-
Length is int(sqrt(1 + (dy/dx)^2)dx)|(0,3) where int represents an integral and sqrt is the square root of what is inside the parenthesis

y = (x^2 + 2)^1.5/3
dy/dx = x(x^2 + 2)^0.5

int(sqrt(1 + x^2(x^2 + 2))dx)|(0,3)
int(sqrt(x^4 + 2x^2 +1)dx)|(0,3)
int(x^2 + 1 dx)|(0,3)
x^3/3 + x |(0,3)
(9 + 3) - (0 + 0) = 12

I hope this helps!

-
The arclength of some curve y =f(x) on the interval [a,b] = ∫√(1 + (dy/dx)²) dx

In this problem:

dy/dx = x√(x² + 2)

Arc-length = ∫√(1 + x²(x² + 2)) dx from 0 to 3

= ∫√(1 + 2x² + x^4) dx from 0 to 3

= ∫(x² + 1) dx from 0 to 3 = x^3/3 + x eval. from 0 to 3 = 9 + 3 = 12
1
keywords: curve,the,of,length,Find,Find the length of the curve
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .