Calculate the integral of f(x, y) = x − y over the region x² + y² ≤ 81, x + y ≥ 9 by changing to polar coordinates. (Use symbolic notation and fractions where needed.) Ib - y) dA= (x -

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Calculate the integral of \( f(x, y) = x - y \) over the region \( x^2 + y^2 \leq 81, \, x + y \geq 9 \) by changing to polar coordinates.

(Use symbolic notation and fractions where needed.)

\[
\iint_D (x - y) \, dA = \underline{\hspace{6cm}}
\]
Transcribed Image Text:Calculate the integral of \( f(x, y) = x - y \) over the region \( x^2 + y^2 \leq 81, \, x + y \geq 9 \) by changing to polar coordinates. (Use symbolic notation and fractions where needed.) \[ \iint_D (x - y) \, dA = \underline{\hspace{6cm}} \]
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