Question

Find the area of the region inside the rose
r=4sin(2x) and inside the circle r=2

Answer 1

x is theta, just used x for convenience, these are polar equations.

Answer 2

for reference https://www.desmos.com/calculator/icbkdjtg2n

Answer 3

the answer approx 9.82

Answer 4

just having trouble finding that area there

Answer 5

i know the bounds for that area are 0 to 5pi/12

Answer 6

wait no i think i see now...

Answer 7

for the that rose petal, it should be from 0 to pi/2, but i gotta somehow subtract out the rest

Answer 8

gonna try something

Answer 9

try this

0->pi/12 : rose petal
pi/12->pi/4 : circle

Answer 10

http://www.wolframalpha.com/input/?i=8*%28%5Cint%5Climits_0%5E%7Bpi%2F12%7D+1%2F2*%284*sin%282t%29%29%5E2+dt+%2B+%5Cint%5Climits_%7Bpi%2F12%7D%5E%7Bpi%2F4%7D+1%2F2*%282%29%5E2+dt%29