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Areas of regions Make a sketch of the region
Chapter 8, Problem 28E(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 lemniscate \(r^2=2 \sin 2\theta\) and outside the circle r = 1
Questions & Answers
QUESTION:
Make a sketch of the region and its bounding curves. Find the area of the region.
The region inside the lemniscate \(r^2=2 \sin 2\theta\) and outside the circle r = 1
ANSWER:Solution 28EStep 1:We find the area between the the lemniscate = 2 sin 2 and inside the circle r = 1The two curves intersect where Then the area becomesThen we just need to double our answer to find the entire area bound by the lemniscate.So... so the area we seek is