2.. The astroid curve below is defined by the parametric equations x(t) = 2 cos³t, y(t) = 2 sin³t. Compute the area enclosed by the astroid. Compute the total area by getting one fourth the area and multiplying the answer by four. Also include a discussion of how the minus sign issue is resolved. Include detailed work showing all the trig identities etc. required to calculate the integral.

Please help me evaluate this integral, I know it needs to go into cylendrical coordinates but I cannot figure out what theta should be?

Use one of the formulas in (5) to find the area under one arch of the cycloid  x = t - sint and y = 1 - cost. Work seen below. How were the parametric equations x = 2pi - t (3) and y = 0 (4) found? This is an explanation of the problem but the work is not 100% clear.

I don't understand why Amo=2(integral) and not 4/(pi)^2. Can you please explain it to me. Thank you