1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Integrate f (x, y) =...

 

Transcribed Image Text:

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Integrate f (x, y) = x over the region in the first quadrant bounded by the lines y = x, y = 2x, x = 1, and x = 2. Sketch the region of integration for the following integral. Reverse the order of integration and then evaluate the resulting integral. 1²10 2 4- y² dx dy Find the volume of the solid that lies below z = ey + e* and above the region in the xy-plane bounded by 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2. Find the volume of the solid under the hyperboloid z = xy and above the triangle in the xy-plane with vertices (2, 1), (5, 1), and (2, 4). Use double integration to find the area in the xy-plane bounded by the curves x = y ² - 1 and x = 2y² - 2. Use double integration to find the area in the xy-plane bounded by the curves y = ln x, y = 2 In x, and the line x = e in the first quadrant. Find the center of mass of a thin plate bounded by the y-axis and the lines y = x and y=2-x if 8 (x, y) = 6x + 3y + 3. Use double integration in polar coordinates to find the volume of the solid that lies below the surface z = 5 + x - y and above the circle x² + y2 = x in the xy-plane. Find the area of the region that lies inside the cardioid r = 1 + cos 0 and outside the circle r = 1 by double integration in polar coordinates. Set up six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane 2x + 3y + z = 6. Evaluate one of the integrals. Find the volume of the solid bounded by the graphs of these equations: the wedge cut from the cylinder x² + y² = 1 by the planes z = -y and z = 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. Integrate f (x, y) = x over the region in the first quadrant bounded by the lines y = x, y = 2x, x = 1, and x = 2. Sketch the region of integration for the following integral. Reverse the order of integration and then evaluate the resulting integral. 1²10 2 4- y² dx dy Find the volume of the solid that lies below z = ey + e* and above the region in the xy-plane bounded by 0 ≤ x ≤ 2 and 0 ≤ y ≤ 2. Find the volume of the solid under the hyperboloid z = xy and above the triangle in the xy-plane with vertices (2, 1), (5, 1), and (2, 4). Use double integration to find the area in the xy-plane bounded by the curves x = y ² - 1 and x = 2y² - 2. Use double integration to find the area in the xy-plane bounded by the curves y = ln x, y = 2 In x, and the line x = e in the first quadrant. Find the center of mass of a thin plate bounded by the y-axis and the lines y = x and y=2-x if 8 (x, y) = 6x + 3y + 3. Use double integration in polar coordinates to find the volume of the solid that lies below the surface z = 5 + x - y and above the circle x² + y2 = x in the xy-plane. Find the area of the region that lies inside the cardioid r = 1 + cos 0 and outside the circle r = 1 by double integration in polar coordinates. Set up six different iterated triple integrals for the volume of the tetrahedron cut from the first octant by the plane 2x + 3y + z = 6. Evaluate one of the integrals. Find the volume of the solid bounded by the graphs of these equations: the wedge cut from the cylinder x² + y² = 1 by the planes z = -y and z = 0.