Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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**Problem 5:** Find \(\iint_D (x+y)^2 \, dx \, dy\), where \(D\) is the shaded region in Fig. 17.2.12. **Details of Figure 17.2.12:** The figure illustrates a Cartesian coordinate system with a shaded triangular region. The boundaries of the region are: - The line \(y = x\). - The line \(x = 1\). - The x-axis (\(y = 0\)). The region is bounded as follows: - From \(x = 0\) to \(x = 1\). - The region is above the x-axis and below the line \(y = x\). **Graph Explanation:** - The x-axis is horizontal, and the y-axis is vertical, meeting at the origin \((0,0)\). - The line \(y = x\) begins from the origin at a 45-degree angle, extending diagonally upwards to the right. - The line \(x = 1\) is vertical, intersecting the x-axis at \(x = 1\). - The shaded region is a right triangle with vertices at \((0,0)\), \((1,0)\), and \((1,1)\).
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Transcribed Image Text:**Problem 5:** Find \(\iint_D (x+y)^2 \, dx \, dy\), where \(D\) is the shaded region in Fig. 17.2.12. **Details of Figure 17.2.12:** The figure illustrates a Cartesian coordinate system with a shaded triangular region. The boundaries of the region are: - The line \(y = x\). - The line \(x = 1\). - The x-axis (\(y = 0\)). The region is bounded as follows: - From \(x = 0\) to \(x = 1\). - The region is above the x-axis and below the line \(y = x\). **Graph Explanation:** - The x-axis is horizontal, and the y-axis is vertical, meeting at the origin \((0,0)\). - The line \(y = x\) begins from the origin at a 45-degree angle, extending diagonally upwards to the right. - The line \(x = 1\) is vertical, intersecting the x-axis at \(x = 1\). - The shaded region is a right triangle with vertices at \((0,0)\), \((1,0)\), and \((1,1)\).
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