# Double Integral in polar coordinates. How do I find the shaded region in the figure and find the values that setup the iterated integral?

I tried this problem and I didn't get the correct answer. Is it because of my rotation? I tried flipping he bounds and I still got an incorrect answer. Someone please help.

### 3 Answers

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- King LeoLv 710 months agoFavorite Answer
.

16 ≤ x² + y² ≤ 25

16 ≤ r² ≤ 25

4 ≤ r ≤ 5

∫∫𝓡 { f(x) dA, where R = { (r, θ) | 4 ≤ r ≤ 5, ½π ≤ θ ≤ 3π/2 }

= ∫(θ=½π to 3π/2) ∫(r=4 to 5 ) f(r cosθ , rsinθ ) r dr dθ

∴

A = 4

B = 5

C = ½π

D = 3π/2

━━━━━

- VamanLv 710 months ago
The integral is r dr dtheta. r integral gives 1/2 r^2. Put the limits you get 9/2. Theta integral is straight forward theta. limits 3 pi/2- pi/2 pi/2. The area is 9/4 pi .

Thank you for the area Vaman! I needed those limits!

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- alexLv 710 months ago
Hint:

C=4

D=5

just need to find the value of A , B

Super useful hint! I really appreciate it Alex! Thank you for helping me out.

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Thank you King Leo for setting it up! Alex is right, ABCD order is different but not a big deal. I was able to write out the integral with your help! Thank you!

A=pi/2

B=3pi/2

C=4

D=5