Solution Found!
Areas of regions Make a sketch of the region
Chapter 8, Problem 27E(choose chapter or problem)
QUESTION:
Make a sketch of the region and its bounding curves. Find the area of the region.
The region inside the rose \(r=4 \sin 2\theta\) and inside the circle r = 2
Questions & Answers
QUESTION:
Make a sketch of the region and its bounding curves. Find the area of the region.
The region inside the rose \(r=4 \sin 2\theta\) and inside the circle r = 2
ANSWER:Solution 27E
Step 1:
We find the area between the the rose r = 4 sin 2θ and inside the circle r = 2
The two curves intersect where
Then the area becomes
Then we just need to double our answer to find the entire area bound by the lemniscate.
So...
so the area we seek is