Problem 1E: Evaluate the line integral, where C is the given curve. 1. C y ds, C: x = t2, y = 2t, 0 t 3 Problem 2E: Evaluate the line integral, where C is the given curve. 2. C (x/y) ds, C: x = t3, y = t4, 1 t 2 Problem 3E: Evaluate the line integral, where C is the given curve. 3. C xy4 ds, C is the right half of the... Problem 4E: Evaluate the line integral, where C is the given curve. 4. C xey ds, C is the line segment from (2,... Problem 5E: Evaluate the line integral, where C is the given curve. 5. C (x2y + sin x) dy, C is the arc of the... Problem 6E: Evaluate the line integral, where C is the given curve. 6. C ex dx, C is the arc of the curve x = y3... Problem 7E: Evaluate the line integral, where C is the given plane curve. 7. C(x+2y)dx+x2dy Problem 8E Problem 9E: Evaluate the line integral, where C is the given space curve. 9. Cx2yds, C:x=cost,y=sint,z=t,0t/2 Problem 10E: Evaluate the line integral, where C is the given space curve. 10. Cy2zds C is the line segment from... Problem 11E: Evaluate the line integral, where C is the given space curve. 11. Cxeyzds C is the line segment from... Problem 12E: Evaluate the line integral, where C is the given space curve. 12.... Problem 13E: Evaluate the line integral, where C is the given space curve. 13. Cxyeyzdy,C:x=t,y=t2,z=t3,0t1 Problem 14E: Evaluate the line integral, where C is the given space curve. 14.... Problem 15E Problem 16E Problem 17E Problem 18E Problem 19E: Let F be the vector field shown in the figure. (a) If C1 is the vertical line segment from (3, 3) to... Problem 20E: The figure shows a vector field F and two curves C1 and C2. Are the line integrals of F over C1, and... Problem 21E Problem 22E Problem 23E: Evaluate the line integral C F dr, where C is given by the vector function r(t). 21. F(x, y, z) =... Problem 24E: Evaluate the line integral C F dr, where C is given by the vector function r(t). 22. F(x, y, z) = x... Problem 25E: Use a calculator or computer to evaluate the line integral correct to four decimal places. 25. CFdr... Problem 26E Problem 27E Problem 28E: Use a calculator or computer to evaluate the line integral correct to four decimal places. 28.... Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E: A thin wire is bent into the shape of a semicircle x2 + y2 = 4, x 0. If the linear density is a... Problem 36E: A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius... Problem 37E Problem 38E Problem 39E: If a wire with linear density (x, y) lies along a plane curve C, its moments of inertia about the x-... Problem 40E: If a wire with linear density (x, y, z) lies along a space curve C, its moments of inertia about the... Problem 41E: Find the work done by the force field F(x, y) = x i + (y + 2) j in moving an object along an arch of... Problem 42E: Find the work done by the force field F(x, y) = x2 i + yex j on a particle that moves along the... Problem 43E: Find the work done by the force field F(x, y, z) = x y2, y z2, z x2 on a particle that moves along... Problem 44E: The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z)... Problem 45E: The position of an object with mass m at time t is r(t) = at2 i + bt3j, 0 t 1. (a) What is the... Problem 46E Problem 47E: A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo with a radius... Problem 48E Problem 49E: (a) Show that a constant force field does zero work on a particle that moves once uniformly around... Problem 50E Problem 51E Problem 52E Problem 53E: An object moves along the curve C shown in the figure from (1, 2) to (9, 8). The lengths of the... Problem 54E: Experiments show that a steady current I in a long wire produces a magnetic field B that is tangent... format_list_bulleted