Please help: find the length of the curve 2y^2 = x^3 from the origin to x=10.

Answer 1

(ds)^2 = (dx)^2 + (dy)^2 ------->

ds = sqrt[(dx)^2 + (dy)^2] =

sqrt[1 + (dy/dx)^2] dx

The curve is defined by:

2y^2 = x^3

we then have that:

4 y dy = 3 x^2 dx ----->

dy/dx = 3/4 x^2/y ----->

(dy/dx)^2 = 9/16 x^4/y^2 =

9/16 x^4/(1/2 x^3) = 9/8 x

So, you have to integrate:

sqrt[1 + 9/8 x] dx

from x = 0 to x = 10.

Answer 2

y^2=1/2x^3
y=�ã1/2x^3
y=1/1.41x^(3/2)
derivative
dy/dx=3/2.82^(1/2)

Answer 3

Correct, so the square of the derivative is

(3/2.82 x^(1/2))^2 = 9/8 x

Answer 4

i got 24.81 would that be correct?

Answer 5

Yes, that's the correct answer, although the way the problem is formulated, you should probably not give a numerical approximation to the exact answer.

Answer 6

ok thanks alot