Question

for my high school, I need to know how to Express the area enclosed by the ellipse x = 2 cos t, y = 4 sin t, 0 ≤ t ≤ 2π as a definite integral in terms of t. and how to Evaluate this integral. and please explain very neatly so I can practice for my AP.

Answer 1

we can use formula

we are given

now, we can set up integral for area

now, we can solve it

now, we can solve each integrals and then combine them

and we get

.............Answer