Please help the questions. Thanks.
Please help the questions. Thanks. 3. Use Green's Theorem to calculate Je y tan’t dx +...
Q1. Evaluate the line integral f (x2 + y2)dx + 2xydy by two methods a) directly, b) using Green's Theorem, where C consists of the arc of the parabola y = x2 from (0,0) to (2,4) and the line segments from (2,4) to (0,4) and from (0,4) to (0,0). [Answer: 0] Q2. Use Green's Theorem to evaluate the line integral $. F. dr or the work done by the force field F(x, y) = (3y - 4x)i +(4x - y)j...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and y-x2 oriented in the positive direction 3. Use the curl test to show that F(x,y)- (x2yi+(y)j is path dependent. 4. Use Green's Theorem to evaluate the line integral , (2x-y)dx-r3)dy where C is the boundary of the region between y = 2x and...
Use Green's Theorem to evaluate the line integral 2xy dx + (2x + y) dy с where C is the circle centered at the origin with radius 1. Start by sketching the region of integration, D.
please answer all 3 questions, I need help. thank you Use Green's Theorem to evaluate the line integral. Assume the curve is oriented counterclockwise. $(9x+ ex) dy- (4y + sinh x) dx, where C is the boundary of the square with vertices (2, 0), (5, 0), (5, 3), and (2, 3). $(9x+ ey?) ay- (4y+ + sinhx) dx = 0 (Type an exact answer.) Use Green's Theorem to evaluate the following line integral. i dy - g dx, where (19)...
Use Green's Theorem to evaluate the line integral. (x - 97) dx + (x + y) dy C: boundary of the region lying between the graphs of x2 + y2 = 1 and x2 + y2 = 81 x-9
Use Green's Theorem to calculate the line integral f. 2xy dx + 2(x+y) dy, where C is the unit circle centered at the origin and it is counter-clockwise oriented. $c 2xy dx + 2(x + y) dy =
4.Use Green's Theorem to evaluate the line integral. ∫C 2xydx + (x + y)dy C: boundary of the region lying between the graphs of y = 0 and y = 1 - x2_______ 5.Use Green's Theorem to evaluate the line integral. ∫C ex cos(2y) dx - 2ex sin(2y) dy C: x2 + y2 = a2 _______
1. Use Green's theorem to evaluate the integral $ xy dx - x^2 y^3 dy, where C is the triangle with vertices (0,0), (1,0) y (1,2)
9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation. 9. (Green's Theorem) Use Green's Theorem to evaluate the line integral -yd xy dy where C is the circle x1 +y½ 49 with counterclockwise orientation.