Questions 4-6. Sorry if it's a lot of work, I don't have alot of time, and I would like to understand how to solve each question individually.(Don't worry I understand question 7) it's 0. Write clearly your steps, your procedure. Work as a team, share your ideas on how to solvethe problem and check your calculations with each other. Draw the regions of integration.1. Evaluatehect2. EvaluateJoxy ds where C is the lower half of the circle x² + y2 = 8 oriented clockwise.C3. EvaluateSo F. dr where F(x, y) = (x - y, 1) and C is the ellipse ²/9 + y² = 1.CJo (x² + y²) dx + 2(x - y)dy where C is the triangle with vertices (0, 0), (2, 6),2Cand (0,6).4. Find a parametrization for the surface given by the part of x = 8 - 2y² - 2z² that liesin front of the plane x = -2.5. Find the area of the surface given by z = 1+ 7x + y² that lies above the trinagle withvertices (0, 0), (0, 3) and (12, 3).6. Use Stoke's theorem to evaluatecurl (F). ds where F(x, y) = (x²y², z, r³y³z) andSS is the part of the paraboloid z = 30- x² - y² that lies above the xy-plane and insidethe cylinder x² + y2 = 9, oriented in the dircetion of the positive z-axis.7. Use Gauss's theorem to evaluate[[ ·curl (F) ds where F(x, y) = (x² + 4xz, -2xy, z²)Sand S is the surface bounded by the two hemispheres z = -√1-x² - y²2 = - -√4x² - y² and the plane z = 0.

According to the Bartleby rules, I can answer only the first question from which you asked as there…

Write clearly your steps, your procedure. Work as a team, share your ideas on how to solve the problem and check your calculations with each other. Draw the regions of integration. 1. Evaluate 2. Evaluate 3. Evaluate Ty ry ds where C is the lower half of the circle x² + y2 = 8 oriented clockwise. [F F. dr where F(x, y) = (x - y, 1) and C is the ellipse x²/9 + y² = 1. and (0,6). (x² + y²)da + 2(x - y)dy where C is the triangle with vertices (0, 0), (2, 6), 4. Find a parametrization for the surface given by the part of x = 8 - 2y2 - 2z² that lies in front of the plane x = -2. 5. Find the area of the surface given by z = 1+ 7x + y² that lies above the trinagle with vertices (0,0), (0, 3) and (12, 3). 6. Use Stoke's theorem to evaluate I cur S S is the part of the paraboloid z = 30-x² - y² that lies above the xy-plane and inside the cylinder x² + y² = 9, oriented in the dircetion of the positive z-axis. curl (F) dS where F(x, y) = (x²y², z, x³y³z) and . 11a curl (F) ds where F(x, y) = (x² + 4xz, -2xy, z² = -√√√1-x² - y² 7. Use Gauss's theorem to evaluate and S is the surface bounded by the two hemispheres z = z = -√√√4-x² - y² and the plane z = 0.

Write clearly your steps, your procedure. Work as a team, share your ideas on how to solve the problem and check your calculations with each other. Draw the regions of integration. 1. Evaluate 2. Evaluate 3. Evaluate Ty ry ds where C is the lower half of the circle x² + y2 = 8 oriented clockwise. [F F. dr where F(x, y) = (x - y, 1) and C is the ellipse x²/9 + y² = 1. and (0,6). (x² + y²)da + 2(x - y)dy where C is the triangle with vertices (0, 0), (2, 6), 4. Find a parametrization for the surface given by the part of x = 8 - 2y2 - 2z² that lies in front of the plane x = -2. 5. Find the area of the surface given by z = 1+ 7x + y² that lies above the trinagle with vertices (0,0), (0, 3) and (12, 3). 6. Use Stoke's theorem to evaluate I cur S S is the part of the paraboloid z = 30-x² - y² that lies above the xy-plane and inside the cylinder x² + y² = 9, oriented in the dircetion of the positive z-axis. curl (F) dS where F(x, y) = (x²y², z, x³y³z) and . 11a curl (F) ds where F(x, y) = (x² + 4xz, -2xy, z² = -√√√1-x² - y² 7. Use Gauss's theorem to evaluate and S is the surface bounded by the two hemispheres z = z = -√√√4-x² - y² and the plane z = 0.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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