.2 L(x² + xy - y²) dy dx. 13.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Evaluate the integrals, sketch and identify the type of the region (corresponding to the way that the integral is written)
13. \[\int_{0}^{1} \int_{0}^{x^2} (x^2 + xy - y^2) \, dy \, dx.\]

Explanation:
This is a double integral which first integrates the function \(x^2 + xy - y^2\) with respect to \(y\) from \(0\) to \(x^2\), and then integrates the result with respect to \(x\) from \(0\) to \(1\).
Transcribed Image Text:13. \[\int_{0}^{1} \int_{0}^{x^2} (x^2 + xy - y^2) \, dy \, dx.\] Explanation: This is a double integral which first integrates the function \(x^2 + xy - y^2\) with respect to \(y\) from \(0\) to \(x^2\), and then integrates the result with respect to \(x\) from \(0\) to \(1\).
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