## TylerD one year ago Find the area of the region inside the rose r=4sin(2x) and inside the circle r=2

1. TylerD

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

2. TylerD

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

3. TylerD

4. TylerD

just having trouble finding that area there

5. TylerD

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

6. TylerD

wait no i think i see now...

7. TylerD

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

8. TylerD

gonna try something

9. ganeshie8

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

10. ganeshie8
11. ganeshie8

|dw:1438072090508:dw|

12. TylerD

i think i see what u did just need to figure out how u factored it, sec.

13. ganeshie8

that bottom "black" area is given by : $\large \int\limits_0^{\pi/12} \frac{1}{2}*(4\sin(2t))^2 ~dt$

14. ganeshie8

the top blue area is given by : $\large \int\limits_{\pi/12}^{\pi/4} \frac{1}{2}*(2)^2 ~dt$

15. TylerD

then you multiplied by 2 then again by 4? for symmetry

16. ganeshie8

Yes

17. TylerD

alright thanks, really appreciated, been stuck on that one for 2 hours.