7-10 Evaluate the double integral. y 7. ²1A, SS -dA, + 8. ff (2x + ff (2x + y) dA, D D = {(x, y) | 0 ≤ x ≤ 4,0 ≤ y ≤ √x}
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7-10 Evaluate the double integral. y 7. ²1A, SS -dA, + 8. ff (2x + ff (2x + y) dA, D D = {(x, y) | 0 ≤ x ≤ 4,0 ≤ y ≤ √x}
svar ow 15-16 Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it's easier. 15. ffy dA, D is bounded by y = x -2, x = y² 16. y²exy dA, D is bounded by y = x, y = 4, x = 0
23-32 Find the volume of the given solid. 23. Under the plane 3x + 2y z = 0 and above the region enclosed by the parabolas y = x² and x = y² 24. Under the surface z = 1 + x²y² and above the region enclosed by x = y² and x = 4 25. Under the surface z = xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2) 26. Enclosed by the paraboloid z = x² + y² + 1 and the planes x = 0, y = 0, z 0, and x + y = 2 = 27. The tetrahedron enclosed by the coordinate planes and the plane 2x + y + z = 4 er3HUDI 28. Bounded by the planes z = x, y = x, x + y = 2, and z = 0 29. Enclosed by the cylinders z = x², y = x² and the planes z = 0, y = 4 30. Bounded by the cylinder y² + z² = 4 and the planes x = 2y, x = 0, z 0 in the first octant 31. Bounded by the cylinder x² + y² = 1 and the planes y = z, x = 0, z 0 in the first octant 32. Bounded by the cylinders x² + y² = ² and y² + z² = p²