Evaluate the line integral g. y² dx – x²dy, where Cis the positively oriented circle of radius 2 centered at the origin.

Q: Find an arc length parametrization of the line y = 2x – 6 %3D |

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Q: Parametrize the osculating circle to y = √x at x = 4.

A: Given that the osculating circle  y = x

Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = <t, t2>That implies,

Q: Verify Stokes' theorem for the helicoid (1, 0) = First, compute the surface integral: = (VF)…

A: Given surface is helicoid whose vector parametric equation is \)" data-mce-style="cursor:…

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: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

A:

Q: Find . F.dr when F(x,y) = (2x,3y²) and C is only the first quadrant part of a circle of radius 3…

A: Let C be a smooth curve and r→t=xti^+ytj^+ztk^ be the position vector of any point x,y,z on C.…

Q: The curve y = sqrt ( 4 - x sq. )  ,-1 < = x < = 1  , is an arc of the circle x sq. +  y sq. =…

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Q: •Evaluate radius 2 25 where c' is a circle of 5²-1 centered at origin and directed cc W ds

A: We have to evaluate where is a circle of radius  centered at origin.

Q: The curve y= 7,0 <x <3; is rotated about the x-axis. Find the exact area of the 3 resulting surface.

A: Given: The curve is Interval is from 0  to 3  and it is rotated about x axis

Q: Evaluate the line integral Say ds, where C is the right half of the circle æ² + y² = 4.

A: We have to evaluate:∫C8xy6dsHere C is the right half of the circle x2+y2=4.

Q: Evaluate [F.dr, where C is the circle x² + y² = 4 oriented counterclockwise and F = (y,-x). Set up…

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Q: Sketch the spiral r = θ for 0 ≤ θ ≤ 2π and find the area bounded by the curve and the first…

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Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 5 sxS 21

A: The equation of the given curve is y=13x32.The curve is bounded between x=5 to x=21.We have to find…

Q: メ y= oL Xとn2

A: Given curve is y=ex , 0≤x≤ln2find the area of the surface

Q: Find the equation of the tangent plane to the surface z = 4.x*y? + 2y at point (1, -2, 12).

A:

Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3

Q: e Lay xy¹ ds where C' is the right half of the circle x² + y² = 9 Evaluate

A: We find required integral by parametrizing x and y .