Calculating areas bounded by polar curves looks extremely difficult. Do Americans really need to integrate such a complex expressions without a calculator?

I am a Japanese and not familiar with a calculus course in the United States.
Looking around Socratic, I found there are so many questions about areas bounded by a polar curve, but few answers are posted.

I know the formula #S=1/2int_alpha^beta{f(theta)}^2d##theta#.
However, this integration looks often beyond our ability, such as in my previous post which I have finally given up.

Some questions seem even more difficult. I wonder how the students in the USA perform such a complex integration without a calculator.

1 Answer
Dec 10, 2017

I'm really not sure who's asking these questions. The linked question is a great example of one.

As an American high schooler, I've never been asked such a complex question for school. I think the goal with those is just to use a calculator. Maybe they're just testing knowledge of the polar area formula. Maybe they're testing calculator skills. Not really sure. I'm still gonna try my best to do the linked problem, though!