5. Compute the line integral ſc fds, where a) C is the line segment from (3,4,0)...
No 3 putin uhd e integral lound a r the val- 0 VIIl, 81. EXERCISES Compute the curve integrals of the vector field over the indicated curves. (x,y)=(x2-2xy,y2-2xy) along the, parabola y=x2 from (-2,4) to 2. 0x, y, xz - y) over the line segment from (0,0, 0) to (1, 2, 4), 3, Let r (x2 y2)1/2 Let F(X)-X. Find the integral of F over the circle of radius 2, taken in counterclock wise direction. 4. Let C be a...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...
Evaluate the line integral. fr de x² dx + y²dy, where C is the arc of the circle x2 + y2 = 4 from (2,0) to (0,2) followed by the line segment from (0, 2) to (4,3).
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...
Thank you! xdy - ydx ф 30v2 where c is the boundary of the 3 Evaluate the line integral 1 segment formed by the arc of the circle x2 +y2-4 and the chord y-2-1 for x 2 0. xdy - ydx ф 30v2 where c is the boundary of the 3 Evaluate the line integral 1 segment formed by the arc of the circle x2 +y2-4 and the chord y-2-1 for x 2 0.
Q5. (10+10+5=25 points) a) Use Green's Theorem to evaluate the line integral $. 3x2ydx - 3xy’dy along the negatively oriented curve C which is the boundary of the region enclosed by upper half of the circle x2 + y2 = 4 and x-axis. b) Evaluate Sc, 3x” ydx – 3xy?dy where C1 is only upper half of the circle x2 + y2 = 4. c) If P = 0, Q = x in part (a), find $ xdy without taking...
Use Green’s Theorem to compute ∮c (2xy−y+ 1) dx+ (x2−ln(1 +y)) dy where C is the top half of the circle x2+y2= 4 along with the line segment connecting (−2,0) and (2,0)
Verify that the line integral and the surface integral of Stokes Theorem are equal far the following vector field, surface S, and closed curve C. Assume that C has counterlockwise orientation and S has a consistentorientation F = 〈y,-x, 11), s is the upper half of the sphere x2 + y2 +22-1 and C is the circle x2 + y2-1 in the xy-plane Construct the line integral of Stokes' Theorem using the parameterization r(t)= 〈cost, sint, O. for 0 sts2r...
THE ANSWER IS NOT 0. NO DECIMALS EXACT ANSWER ONLY Find the line integral ſc (3x + 4y) ds along the curve C, which is given by x = sin (31), y = 5 sin (3t), and 0 sts (Express numbers in exact form. Use symbolic notation and fractions where needed.) | 3x (3x + 4y) ds =
i need help with all parts. i will rate. thank you very much. Let C be the closed curve consisting of two pieces. One piece is the upper-half circle of radius 3, centered at the origin, oriented counter-clockwise. The other piece is the horizontal line segment from (-3,0) to (3,0). Evaluate the line integral $ (x2 + y2)dx + (6xy—y?)dy = с (-3,0) (3,0) O 36 O 72 O 31 91/2 The level set of f(x,y) = 12 is a...