Q2 Calculate 8- z dz, z(4-z)* where C is the circle of radius 7, centre 0, negatively oriented.

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

A:

Q: Find the area of the surface generated when the curve y [2,4] is rotated about the y-axis.

A:

Q: 4. Find the area of the plane region that lies below the line y = 2x and between the parabolas y =…

A: The area between two curves y=f(x) and y=g(x) within the x-limits x=a to x=b is given by:…

Q: Evaluate ſf, (3x + 4y²) dA where R is the region in the upper half - plane bounded by the circles x²…

A: As the areas are circular thus convert the integral into polar form. Now determine the limits of the…

Q: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

Q: (b) Find the circle of curvature at (0, 1)of the curve y = x3 + 2x² + x +1

A:

Q: Integrate f(z) = 1 Z³-Z4 clockwise around the circle C: |z| 1 NIT 2

A:

Q: Calculate 8-z -dz, z(4-z) where C is the circle of radius 7, centre 0, negatively oriented.

A: C : circle with radius 7 and centre 0, negatively oriented  f(z) = (8-z)/(z(4-z)) Singularity of…

Q: 10. Evaluate , (2x – y) dA where D is bounded by the circle with center the origin and radius 2.

A:

Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: Calculate the line integral ∫Cy2ds, where C is a part of the circle x=acost, y=asint, 0≤t≤π/2.

A:

Q: B- Find the area of the surface generated by revolving the curve y = √√2-x² about x-axis

A: Introduction:   An object's surface area is the total area that all of its surfaces occupy. The…

Q: Find the area of the inner loop of the curve r= 1-2cos θ

A: For the inner loop of the curve 1-2cos θ=0⇒2cos θ=1⇒cos θ=12⇒θ=cos-112⇒θ=π3,5π3

Q: Compute the surface area of the portion of the hyperboloid x² + y? -? = 64 between z = 7 and z = 8.

A:

Q: Find the area of ​​the rotating surface that occurs by turning circle x2+y2=4 around line x=2 .

A:

Q: find the Volumae of soliel generated by revolving the region in the first quadsant bonended by y=X…

A: The volume of revolution generated by full revolution of the area A between the curves y1=f1(x) and…

Q: Find &y:3mは や Rirst * = In in the the between the Curve area the line メ=H quadraut

A: We first sketch the region using a graphing calculator

Q: Q2 Calculate 8 - z dz, (4- | where C is the circle of radius 7, centre 0, negatively oriented.

A:

Q: Find the area of the surface generated by revolving the curve about each given axis. x= 5t, y- 9t,…

A:

Q: Sketch the surface given by the function. z = 9-x?-y?

A: Given, z=9-x2-y2

Q: 4) Find the families of lines of curvature of the surface z = r + y? .

A: Given: z=x2+y2

Q: Find all points on the isometric dot plane, Ax,1 yl, with x and y integers, that are ex- actly V133…

A: a)The distance from origin to point x,y is 133. b)The distance from origin to point x,y is 217.

Q: 4. Evaluate √3x²e¹² da + 2x¹yev dy where the open curve C is the semicircle x² + y² = 5, y ≥ 0 going…

A: 4. The given integral is ∫C 3x2ey2dx +2x3yey2dy where C is the semicircle x2+y2=5, y≥0 To find: the…

Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

A:

Q: 4. If the curve y = 3 – x², 0<x<4 is rotated about the y-axis, find the area of the resulting…

A:

Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

A:

Q: Find the surface area of the cone frustum generated by revolving the line segment y = 4 1 over 1 < x…

A:

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: F = (y + 2x, 2x + 5z, 1y + 8x), C is the circle with radius 5, center at (2, 0, 0), in the plane x =…

A: F=y+2x, 2x+52, 7y+8xCircle centered at (2, 0, 0) and radius is 5In x=2 planeOrientation- counter…

Q: 2. Find the area of the surface generated by revolving the curve r = Vcos 20, 0s0 ST/4. about the y…

A: Surface area generated by revolving the curve 'r' about y-axis = 2π∫αβxr2+(drdθ)2 dθ

Q: 4. Find the area of the surface generated by revolving the curve y = v9 – x², - 2 < x < 2, about the…

A:

Q: Evaluate the exact area of the surface obtained by rotating the circle x2 + y² = r² about the line y…

A:

Q: How many square units is the area of the surface obtained by rotating the curve y = V4-z, 0 <I<2…

A:

Q: Determine the shortest distance from the surface xy+3x+z2=12 to the origin.

A: Given surface equation is

Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

A:

Q: 157. Calculate -x²ydx + xy? dy, where C is a circle of radius 2 centered at the origin and oriented…

A:

Q: ston Compute the length of the circle of radius r defined parametrically by x = 3 cost, y = 3 sint ;…

A: given that x=3 cost , y=3 sint; 0≤t≤2π find out the length of the circle of radius r i.e. arc length…

Q: Find the area of the surface obtained by rotating the circle x^2+y^2=r^2 about the line y=2r

A:

Q: 7. Find the surface area of the cone frustum generated by revolving the line segment x 1 y ==+ 1s…

A:

Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

A: Here I am attaching image so that you understand each and every step.

Q: Integrate counterclockwise dz, C' the circle with z² + 8z + 15 center -3 and radius 2. dz = La z2 +…

A:

Q: Express you answer in Mdx + Ndy = 0. 1. Circles whose center is passing through y = 4x %3D

A:

Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: The area of the surface obtained by rotating the curve y = 36-x2, -6<xS6 about the x-axis is

A:

Q: 7. Find the area of the portion of the plane z = 2 y that lies directly above the circle x+(y-1) =1…

A:

Q: the line integral SexY² ds where C is the of the Circle x² + y²=4 oriented clockwise Evaluate Cight…

A:

Q: The area of the surface generated by revolving the curve y = y9 - x2,-2 < x < 2 about the x-axis is…

A:

Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

A: we have to find area of the portion of plane .and coverting the problem in polar coordinate makes it…

Q: Find the area of the surface obtained by rotating the curve y² = 4x + 4 0<x<8 about the x-axis?

A: