Use version 2 of the arc length formula to find the length of the curve defined by

Question

Use version 2 of the arc length formula to find the length of the curve defined by 16xy^2 - y^6 = 8 from (9/16, 1) to (9/8, 2)

x = 1/2y^2 + y^4/16

dy/dt = -1/y^3 + y^3/4

integral sign upper bound 2 lower bound 1 sqrt(1 + (y^3/4 -1/y^3)^2

integral sign upper bound 2 lower bound 1 sqrt((y^3/4 +1/y^3)2

integral sign upper bound 2 lower bound y^3/4+1/y^3

antiderivative = y^4/16 - 1/2y^2

then I evaluate the integral and get - 21/16 as the answer but my assignment is counting it wrong

Answer 1

16xy² - y⁶ = 8

16xy² = y⁶ + 8

x = (y⁶ / 16y² + 8 / (16y²)

x = (y⁴ / 16) + (y^-2 / 2)

Maybe that is the source of the error?