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## Homework Statement

Evaluate ∫∫

_{D}(3x + 4y 2 ) dA, where D = {(x, y) : y ≥ 0, 1 ≤ x 2 + y 2 ≤ 4} with the use of polar coordinates.

## Homework Equations

## The Attempt at a Solution

I made a sketch of the circle. It's radius is = 1 and it's lowest point is at (0,0), highest at (0,2), leftmost point at (-1,1) and rightmost point at (1,1).

Converting this integral into polar coordinates:

∫∫

_{D}(3rcosθ+4(rsinθ)

^{2}) r dr dθ

then distributing the r

∫∫

_{D}(3r

^{2}cosθ+4r(rsinθ)

^{2}) dr dθ

The outside integral goes from 0≤θ≤2π

I'm not totally sure with the inside integral though.

0≤r≤1? Because the maximum that the radius is is 1?

I haven't evaluated it yet. I want to make sure I've set it up correctly first. :)