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Get solution: 5057. Miscellaneous integrals Evaluate the following integrals using the
Chapter 13, Problem 56(choose chapter or problem)
QUESTION:
Evaluate the following integrals using the method of your choice. A sketch is helpful.
\(\iint_{R} \frac{x-y}{x^{2}+y^{2}+1} d A\); R is the region bounded by the unit circle centered at the origin.
Questions & Answers
QUESTION:
Evaluate the following integrals using the method of your choice. A sketch is helpful.
\(\iint_{R} \frac{x-y}{x^{2}+y^{2}+1} d A\); R is the region bounded by the unit circle centered at the origin.
ANSWER:Step 1 of 4
\(\begin{array}{l} \int_{R} \int \frac{x-y}{x^{2}+y^{2}+1} d A \\ R=\left\{(x, y): x^{2}+y^{2} \leqslant 1\right\}=\{(r, \theta): 0 \leqslant \theta \leqslant 2 \pi, r \leqslant 1\} \end{array}\)