Question

Polar region:
Find the area bounded by r=2+sin4(theta)

Answer 1

here's the graph

Answer 2

An integral should do it :)

Answer 3

I think we just take integral on one loop and then multiple by 4 to get the answer, right? @Kurd

Answer 4

\[\int_{0}^{\pi/2}(2+sin 4\theta) d\theta\]

Answer 5

and it is not hard to find out the result.

Answer 6

I'm flattered that you actually remember my name :D
...almost.

I suggest just get the integral all the way from 0 to 2pi.

Answer 7

either ways work well. :) since the graph is symmetric.

Answer 8

what if I use 7pi/6 and pi/6 as my higher and lower limits is that okay?

Answer 9

you are looking for area, not arc length, of one full loop. A = ∑∆A = ∑(1/2)r^2∆ø = 1/2∫r^2 dø

of course it looks symmetric but i do not see why you should not just use a normal interval.

Answer 10

yep.

Answer 11

yes, we have the same answer :)

Answer 12

thanks. God Bless O:) to all of you