Question

Find the length of the curve given parametrically by x = cos^3 (θ) , y = sin^3 (θ) between θ = 0 and θ = π .

Answer 1

hello

Answer 2

\[\int\limits_{0}^{\pi} \sqrt{(\frac{dx}{d \theta})^2+(\frac{dy}{d \theta})^2} d \theta\]

Answer 3

that should be the integral representation of the length of the parametric curve x=x(theta)
and y=y(theta) where theta is in [0,pi]

Answer 4

Can you differentiate both of your equations w.r.t to theta?

Answer 5

differentiating x=cos^3 (theta) would give 3cos^2 (theta)* sin(theta)
differentiating y=sin^3 (theta) would give 3sin^2(theta) * -cos (theta)

Answer 6

the first term is - , the second term is + . However, still have 4 more steps,
1) square them
2) add them
3)square root them
4) integrate them.