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PLEASE HELP!! TRYING TO PREPARE FOR A TEST!! TOTAL 50 POINTS WHEN GIVEN BRAINLIEST ANSWER!!
Change the Cartesian integral to an equivalent polar integral, and then evaluate. ∫₋₁₁¹¹ ∫₀√⁽¹²¹⁻ˣ²⁾ dy dx
\int\limits^{11}_{-11} \int\limits^{\sqrt{121-x^{2}} } _{0} dy dx
The key is recognizing the domain of integration as the semicircle centered at the origin with radius 11. In polar coordinates, this integral transforms to
[tex]\displaystyle \boxed{\int_0^\pi \int_0^{11} r \, dr \, d\theta}[/tex]
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