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8. Find the r-coordinate of the center of mass of the lamina that occupies the region D = {(r, y) | 0

8. Find the r-coordinate of the center of mass of the lamina that occupies the region D = {(r, y) | 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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please do question 8

Sea 1. Use a Riemann sum with m = 3 and n = 2 to estimate the value of (x+ 2y) dA where R R= [0, 6] × [0, 2]. Take sample points to be the lower right corners. -2 Compute /. yev? 2. dx dy. + x2 3. Compute // 3ry? dy da. 4. Compute L 6xyz dz dr dy. 5. Compute / cos(y) dy dx by reversing the order of integration. 6. Find the volume of the solid bounded by the paraboloids z = a? + y? and z = 2 – x2 - y?. TY 7. Compute dy dx by converting to polar coordinates. VT2 + y? 4-12 8. Find the x-coordinate of the center of mass of the lamina that occupies the region D {(x, y) | 0<x < 1, x² < y < 1} and has density function p(x, y) = x + y. 9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle R = [0,2] × [-3, 3]. cln 4 cln 3 cln 2 10. Compute e0.5x+y-z dz dy dx. 11. Find /// ?y dV where E is the solid bounded by the cylinder y = x2 and the planes z = 0, y = 1, and z = y. %3D 12. Find the volume of the solid bounded by the cylinder x2 + y² = 4 and the planes z = 0 and y + z = 3. -2 4-y2 4-x2-y2 13. Compute y? Vx2 + y2 + z2 dz dx dy by converting to spherical 4-22-y2 coordinates. 14. A sphere of radius k has a volume of Tk. Set up the iterated integrals in rectangular, cylindrical, and spherical coordinates needed to compute this.
Transcribed Image Text:Sea 1. Use a Riemann sum with m = 3 and n = 2 to estimate the value of (x+ 2y) dA where R R= [0, 6] × [0, 2]. Take sample points to be the lower right corners. -2 Compute /. yev? 2. dx dy. + x2 3. Compute // 3ry? dy da. 4. Compute L 6xyz dz dr dy. 5. Compute / cos(y) dy dx by reversing the order of integration. 6. Find the volume of the solid bounded by the paraboloids z = a? + y? and z = 2 – x2 - y?. TY 7. Compute dy dx by converting to polar coordinates. VT2 + y? 4-12 8. Find the x-coordinate of the center of mass of the lamina that occupies the region D {(x, y) | 0<x < 1, x² < y < 1} and has density function p(x, y) = x + y. 9. Find the surface area of the part of the cylinder y? + z2 = 9 that is above the rectangle R = [0,2] × [-3, 3]. cln 4 cln 3 cln 2 10. Compute e0.5x+y-z dz dy dx. 11. Find /// ?y dV where E is the solid bounded by the cylinder y = x2 and the planes z = 0, y = 1, and z = y. %3D 12. Find the volume of the solid bounded by the cylinder x2 + y² = 4 and the planes z = 0 and y + z = 3. -2 4-y2 4-x2-y2 13. Compute y? Vx2 + y2 + z2 dz dx dy by converting to spherical 4-22-y2 coordinates. 14. A sphere of radius k has a volume of Tk. Set up the iterated integrals in rectangular, cylindrical, and spherical coordinates needed to compute this.
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