whatlifeforme said:Homework Statement
find the length of the curve.Homework Equations
x=y^3/15 + 5/4y on 3<=y<=5
The Attempt at a Solution
(dy/dx)^2 = Y^4/25 - 1/2 + 25/16y^4
integral (3,5) y^2/5 + 5/4y^2
however, i got the wrong answer. the answer is 67/10.
The formula for finding the length of a curve with the equation Y^3/15 + 5/4y is the arc length formula, which is given by L = ∫√(1 + (dy/dx)^2)dx.
To find the derivative of Y^3/15 + 5/4y, first rewrite the equation as (1/15)y^3 + (5/4)y. Then, use the power rule to find the derivative, which is given by dy/dx = (3/15)y^2 + (5/4).
Yes, this equation can be solved using integration. The arc length formula involves integration in order to find the length of a curve.
The limits of integration for this equation depend on the given curve and the range of values for y. They can be determined by looking at the starting and ending points of the curve.
No, the arc length formula is the most accurate way to find the length of a curve with this equation. However, if the equation is in a simpler form, there may be other methods to find the length of the curve, such as using the Pythagorean theorem.