(1 point) If C is the line segment from (7,4) to, (0,0), find the value of...
(1 point) If C is the line segment from (7,4) to, (0,0), find the value of the line integral: Sc(3y2 7 + 2x1).dñ = ī (1 point) Find Sc((x2 + 3y)i + 5y37) . • dr where C consists of the three line segments from (1,0,0) to (1,1,0) to (0,1,0) to (0,1, 3). Sc((x2 + 3y)ī + 5y37). . dr =
(1 point) Let Vf =-8xe-r sin(5y) 20e-x. cos(Sy) j. Find the change inf between (0,0) and (1, π/2) in two ways vf . dr, where C is a curve connecting (0,0) and (1.d2). (a) First, find the change by computing the line integral The simplest curve is the line segment joining these points. Parameterize it: with 03t s 1, r(t)- so that Icvf . di- Note that this isn't a very pleasant integral to evaluate by hand (though we could...
→ (1 point) Let Vf-6xe-r sin(5y) +1 5e* cos(Sy) j. Find the change inf between (0,0) and (1, n/2) in two ways. (a) First, find the change by computing the line integral c Vf di, where C is a curve connecting (0,0) and (1, π/2) The simplest curve is the line segment joining these points. Parameterize it: with 0 t 1, K) = dt Note that this isn't a very pleasant integral to evaluate by hand (though we could easily...
5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3) 5. Evaluate the integral c (2x -y)dx + (x + 3y)dy along the path C: line segment from (0,0) to (3,0) and (3,0) to (3,3)
(1) Evaluate the following line integrals in R3. r +yds for C the line segment from (0, 1,0) to (1, 0,0) for C the line segment from (0,1,1) to (1,0,1). for C the circle (0, a cos t, a sin t) for O (iv) 2π, with a a positive constant. t for C the curve (cost +tsint,sint tcost, 0) for Osts v3 (Hint for (i): use the parametrization (z, y, z) = (t, 1-t, 0) for 0 1) t (1)...
Please help solve the following question with steps. Thank you! 6. Compute JF . T ds where F (-y,z) and (a) C is the line segment from (1,0) to (0,0) followed by the line segment from (0,0) to (0, 1) (b) C is the line segment from (1,0) to (0, 1) (c) C is the part of the unit circle in the first quadrant, moving from 6. Compute JF . T ds where F (-y,z) and (a) C is the...
9. (a) Find a parametrization for the line segment from the point (-1, 2) to the point (3,-2). given (b) Find the length of the line segment using techniques learned in chapter 11. (Note: No credit will for using the Pythagorean theorem to find the length).
9. (a) Find a parametrization for the line segment from the point (-1, 2) to the point (3,-2). (b) Find the length of the line segment using techniques learned in chapter 11. (Note: No credit will be given for using the Pythagorean theorem to find the length).
1 point) The path C is a line segment of length 39 in the plane starting at (2,1). For f(z, y)- 5x 12y, consider (a) Where should the other end of the line segment C be placed to maximize the value of the integral? Atx= , y (b) What is the maximum value of the integral? maximum value- 1 point) The path C is a line segment of length 39 in the plane starting at (2,1). For f(z, y)- 5x...
find the average value of the following function Evaluate the following line integral along each path C--G is the line segment from (-5,-3) to (0,2). C Gis the arc ofthe parabola x-4-y2from (-5,-3)to (0,2) a. b. from (5,- 3) (12 points)|y'dx+ xdy Evaluate the following line integral along each path C--G is the line segment from (-5,-3) to (0,2). C Gis the arc ofthe parabola x-4-y2from (-5,-3)to (0,2) a. b. from (5,- 3) (12 points)|y'dx+ xdy