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.

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  • 10 months ago
    Favorite 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

    ━━━━━

    • iplayer78610 months agoReport

      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

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  • Vaman
    Lv 7
    10 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 .

    • iplayer78610 months agoReport

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

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  • alex
    Lv 7
    10 months ago

    Hint:

    C=4

    D=5

    just need to find the value of A , B

    • iplayer78610 months agoReport

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

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