Problem 1E: Evaluate the line integral, where C is the given curve. cyds,C:x=t2,y=2t,0t3 Problem 2E: Evaluate the line integral, where C is the given curve. c(x/y)ds,C:x=t3,y=t4,1t2 Problem 3E: Evaluate the line integral, where C is the given curve. cxy4ds,C is the right half of the circle... Problem 4E Problem 5E: Evaluate the line integral, where C is the given curve. c(x2y+sinx)dy, C is the arc of the parabola... Problem 6E: Evaluate the line integral, where C is the given curve. Cexdx, C is the arc of the curve x=y3 from... Problem 7E: Evaluate the line integral, where C is the given curve. c(x+2y)dx+x2dy, C consists of line segments... Problem 8E: Evaluate the line integral, where C is the given curve. cx2dx+y2dy, C consists of the arc of the... Problem 9E: Evaluate the line integral, where C is the given curve. cx2yds, C:x=cost,y=sint,z=t,0t/2 Problem 10E: Evaluate the line integral, where C is the given curve. Cy2zds, C is the line segment from (3,1,2)... Problem 11E: Evaluate the line integral, where C is the given curve. cxeyzds, C is the line segment from (0,0,0)... Problem 12E: Evaluate the line integral, where C is the given curve. C(x2+y2+z2)ds, C:x=t,y=cos2t,z=sin2t,0t2 Problem 13E: Evaluate the line integral, where C is the given curve. cxyeyzdy,C:x=t,y=t2,z=t3,0t1 Problem 14E Problem 15E: Evaluate the line integral, where C is the given curve. cz2dx+x2dy+y2dz, C is the line segment from... Problem 16E Problem 17E: Let F be the vector fields shown in the figure. a If C1 is the vertical line segment from (3,3) to... Problem 18E: The figure shows a vector field F and two curves C1 and C2. Are the line integrals of F over C1 and... Problem 19E Problem 20E Problem 21E Problem 22E: Evaluate the line integral CFdr, where C is given by the vector function r(t). F(x,y,z)=xi+yj+xyk,... Problem 23E Problem 24E Problem 25E Problem 26E Problem 27E: Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is... Problem 28E: Use a graph of the vector field F and the curve C to guess whether the line integral of F over C is... Problem 29E: a Evaluate the line integral CFdr, where F(x,y)=ex1i+xyj and C is given by r(t)=t2i+t3j,0t1. b... Problem 30E: a Evaluate the line integral CFdr, where F(x,y,z)=xizj+yk and C is given by r(t)=2ti+3tjt2k,1t1. b... Problem 31E: Find the exact value of Cx3y3zds, where C is the curve with parametric equations... Problem 32E: a Find the work done by the force field F(x,y)=x2i+xyj on a particle that moves once around the... Problem 33E: A thin wire is bent into the shape of a semicircle x2+y2=4,x0. If the linear density is a constant... Problem 34E: A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius... Problem 35E: a Write the formulas similar to Equations 4 for the center of mass (x,y,z) of a thin wire in the... Problem 36E: Find the mass and center of mass of a wire in the shape of the helix x=t,y=cost,z=sint,0t2, if the... Problem 37E Problem 38E Problem 39E: Find the work done by the force field F(x,y)=xi+(y+2)j in moving an object along an arch of the... Problem 40E: Find the work done by the force field F(x,y)=x2i+yexj on a particle that moves along the parabola... Problem 41E Problem 42E Problem 43E Problem 44E: An object with mass m moves with position function r(t)=asinti+bcostj+ctk,0t/2 Find the work done on... Problem 45E: A 160-lb man carries a 25-lb can of paint up a helical staircase that encircles a silo with a radius... Problem 46E Problem 47E: a Show that a constant force field does zero work on a particle that moves once uniformly around the... Problem 48E Problem 49E: If C is a smooth curve given by a vector function r(t),atb and v is a constant vector, show that... Problem 50E Problem 51E: An object moves along the curve C shown in the figure from 1, 2 to 9, 8. The lengths of the vectors... Problem 52E: Experiments show that a steady current I in a long wire produces a magnetic field B that is tangent... format_list_bulleted