6. Evaluate the integral fF ds, for F = (-y, x, z) and C is the circle a? + y? = 2,2 = 1.

Q: dz The value of integral where C is a circle |z-2= 1 z2 - 2z

A: Introduction :

Q: Compute the line integral (Баллов: 2) Jo ds, Cis the right half of circle x2 + y 16 (counter…

A:

Q: Find the line integral ye-xz ds Here, C is the path r(t) = [t,3t,-6t], 0sts In(8) ·

A:

Q: Apply Green's Theorem to evaluate the integral. (8y + x)dx + (y + 3x)dy C: The circle (x - 9)² + (y…

A:

Q: Evaluate the integral x² dx + y? dy where C consists of the arc of the circle x2 + y² = 4 from (2,0)…

A:

Q: 5. Find the following path integral. C is one-eighth of a circle as shown. J x dx (Here Q(x, y) 0…

A: If C is one -eighth of circle shown in figure, we have to evaluate the following integral

Q: 1. Let C be a path along the upper half of a circle from the point P(2,0) to the point Q(-2,0).…

A:

Q: Compute the line integral -xdy + ydx 2(x-y)2 +4xy where L is the circle (1-x)2 + y2 = 3 with a…

A: We can write the given line integral as ∫L y2x-y2+4xydx+-x2x-y2+4xydy, where L is the circle…

Q: Use Green's theorem to evaluate O(1-y') dx+(x³ +e" ) dy , where C is the boundary of the region…

A: The integral is ∮C1-y3dx+x3+ey2dy where C is the boundary of the region between the circles x2+y2=4…

Q: Evaluate the integral ∫C xy2ds, where C is the part of the unit circle x2+y2=4 in the first…

A: Use parametric to solve this

Q: State two other forms for the line integral ∫C F ⋅ n ds given that F = ⟨ƒ, g, h⟩ .

A:

Q: Evaluate cos z dz , where C is the circle |z – 1| = 3. (Integrate counterclockwise around C.)

A:

Q: How do I evaluate this?

A: Let C be the quarter circle centered at (2,0) that goes from (1,0) to (2,1).

Q: 2. Evaluate directly the line integral fo a dy where C is the quarter-circle from (0, 4) to (4, 0)…

A:

Q: Compute the line integral -xdy + ydx 2(x-y)2 + 4xy where L is the circle (1-x)2 + y? 3 with a…

A: We will find parametric equation of L and then convert whole equation in parametric form

Q: 5. Evaluate the double integral (2x – y) dA where D is bounded by the circle with the origin as its…

A:

Q: If C is the line segment from (1,3) to, (0, 0), find the value of the line integral: S(3y² i +3x}) ·…

A:

Q: c) Evaluate the line integral (x+2y)dx -2xdy along the following closed path, the circle x+ y= 25,…

A: In parametric form,

Q: 45. If A = (y – 2x )1 + (3x + 2y)j, compute the circulation of A about a circle C in the xy plane…

A:

Q: Apply Green's Theorem to evaluate the integral. fror (13y + x)dx + (y + 9x)dy C: The circle (x- 5)?…

A:

Q: Apply Green's Theorem to evaluate the integral. (3y + x) dx + (y + 5x)dy C: The circle (x - 2)² +…

A:

Q: 2 Use Green's Theorem to evaluate Jx*ydx-xy dy, where C is the circle 2+ y? – 2601 with…

A: Let be the vector field and C be the boundary of the region D. The Green's theorem states that .

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dĩ (6) where C is the…

A: (6) Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: The shaded area shown in (Figure 1) is bounded by y axis and the curve y? = (1.44 – x) m, where z is…

A:

Q: 3. Evaluate ox?y dx + xy? dy using Green's y 2 Theorem, where C is positively oriented by line y =x…

A:

Q: If the region R is bounded between two circles x² + y = 4, x² + y = 9, then we have: sin(Vx2 + y?)…

A:

Q: Evaluate the following line integral. xy ds; C is the portion of the unit circle r(s) = (cos s, sin…

A: Here we have to evaluate the following line integral,  I=∫Cxyds; C is the portion of the unit circle…

Q: Use Green's Theorem to evaluate the integral Sc(5 sin y – 3y, 2 + 5x cos y) · dr where C is the line…

A: Use Green's Theorem to evaluate the integral ∫C5sin(y)-3y,2+5xcos(y)·dr→, where C is the line…

Q: If C is the line segment from (1, 5) to, (0,0), find the value of the line integral: So(4y? i + 4x…

A:

Q: 3. Evaluate the integral *zp- where C is the circle |2| = 2.

A:

Q: 2. Find the value of the integral of g(z) around the circle |z- il = 2 in the positive sense when 1…

A: Cauchy integral formulae: Let us define function f: D→ℂ and a∈D and 'C' is any closed curve around…

Q: Evaluate the line integral |(2? + y) dx – x dy where C is the line segment from (2,5) to (5,9) in…

A:

Q: c). For each of the given paths, verify Green's Theorem by showing that [y³dx + xºdy=ff(xXx dA.…

A:

Q: Evaluate the line integral ſc(4y+ tan? x)dx + (6x – evsin´y)dy over curve C that is the circle x2 +…

A: Green's theorem problem....

Q: Calculate the following double integral as the inside of the circle R: x² + y² = 1.

A:

Q: (3z+1) z'e (b) $1+2 z'e² (a) p- - dz -dz 3 (s + z7)(1– z)z?

A: Evaluate the given two integrals over the circle z=4 (a) Let fz=3z+12zz-12z+5 The singularities of…

Q: dz ; C is a circle Iz-1| = 1/2 z4-1 z2

A:

Q: If the region R is bounded between two circles x2 +y? = 1 and x²+y? = 16 , then we have: J| x²+y?)…

A: Let's find.

Q: Compute the line integral f, x?dx + y²dy where the path C consists of the arc of the circle x? + y?…

A: Here we solve the given problem of integral.

Q: . SS, xcos(y)dA, D is bounded by y = 0,y = x² ,x = 1.

A: See the details solution in below

Q: Evaluate the line integral Levis where C is the half circle x² + y² = 1, y ≥ 0. x² + y² ds

A:

Q: If C is the line segment from (8, 1) to, (0,0), find the value of the line integral: Se(8y² i+x3) ·…

A: First we have to write the equation of the line segment C and then convert the given line integral…

Q: Calculate the double integral ∬R(x2+y2)dxdy in the circle x2+y2=2x.

A: Write the equation of circle into standard form. The radius of the circle is 1.

Q: Evaluate the line integral 2xyz dx + x²z dy + x?y dz where C is an oriented simple curve connecting…

A:

Q: 3. (a) Use Green's theorem to evaluate the line integral 4 y* dx – a* dy where C is the positively…

A:

Q: i Apply Green's theorem to eve luate S [rex=y)dx +Cx+g)dy], where C is the bocundaug qxis aiad the…

A:

Q: We want to evaluate P, F · dr, where F(x, y) = and C is the circle x² +y² = 1, oriented clockwise.…

A:

Q: I = Examine the given integral dz ;C z-i -|= 2 the circle

A:

Q: Apply Green's Theorem to evaluate the integral. $(8y + x)dx +x)dx + (y + 7x)dy C $(BY+x +x)dx + (y +…

A: