g) div(7) for 7(x, y,z) = xyi + yz²j +x²yzk h) curl(ï) for ū(x, y, z) = xzi + xy²j+y²zk

Q: Find the surface area of z=x2+y above the triangle with vertices (0,0),(2,0),(2,2)?

A: The surface area of a function z=f(x,y) over a region D is given by: Surface Area= ∬D ∂z∂x2+∂z∂y2+1…

Q: Express integral I y + x (-4x-2y) -0,x= 1 and y=0,y-1-xto T. of u- dydx in terms of (u)and (v) given…

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Q: Find the centroid of the solid bounded by x² = 4y and y = 5x - x² about the x-axis.

A: We will draw the region and rotate it about x-axis to create a solid of revolution . We will need…

Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

Q: Determine the centroid C (x,y) of the shaded region bounded by (y-20)^2 =16x, and the axes

A: Given : Region bounded by curve (y-20)2=16x and axes.   To find : Centroid C (x,y) of the given…

Q: 3 - Find the bounded ly y=2x-2, x=-1, x= 2 3 area y=2X - 2, x=-I, x= 2 4- Find the anea bondol .

A: Integrate the given parabola from x=-1 to x=2

Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

A:

Q: Find the centroid (¯x,¯y) of the region bounded by: y=8x2+9x,   y=0,   x=0,   and    y=0,   x=0,…

A: Given data: The first function given is f(x)=8x2+9x. The second function given is g(x)=0. The given…

Q: IntegrateF(x, y, z) = z, over the portion of the plane x + y + z = 4 that lies above the square…

A:

Q: Use Stokes' Theorem to find the line integral of F = 3yi + 2zj + 5xk around the triangle obtained by…

A: Given function is F→=3yi^+2zj^+5xk^. We have to evaluate the line integral of F→ around the triangle…

Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices…

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Q: Compute the rotated area bounded by y = 2x, y = 8 about line x = 3 Compute the rotated area bounded…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Calculate the surface area of the z=x²+y surface on the triangular region with vertices (0,0), (1,0)…

A: Let z=fx,y. Differentiate the function fx,y with respect to x and y, to obtain fxx,y and fyx,y.…

Q: . The solid bounded by z = 1 – x², z = 5 – 2x², y = 0, and y – z = 6. |

A:

Q: 2. The region bounded by x = 2 y, x = 0, y = 9 is rotated about the y - axis.

A: Given Data: The given curve is x=2y. Rotated about y axis. The limit for y axis is (0, 9).

Q: (०हागो 10,3,0)and (0,0,6). Tongular lamina with for of stokes deo theorem.

A: Given

Q: (Choose from: a. Disk Method, b.Washer Method, c. Shell Method, d. Disk and Washer, e. Disk and…

A: 1. The bounded region is as follows: In this case the rotation is about x-axis, so, washer method…

Q: Find an equation of the plane passing through the point (1,4,2) with a normal vector of the form n=…

A:

Q: Find the area of the portion of the plane in the first octant passing through the points (0,0,6),…

A: This question can be solved using the area of triangle in three dimensional geometry.

Q: Find the centroid (x¯,y¯)(x¯,y¯) of the region bounded by: y=7x^2+2x,   y=0,   x=0,   and   x=9?

A:

Q: A region R consists of a square bounded by the lines x = -1, x = 1, y = 0, and y = -2 and a half…

A: The given region is as follows: The area of region is  A=∬RdA  =Area of semi-circle of radius…

Q: Use cross products to find the area of the quadrilateral in the xy-plane defined by (0, 0), (1, −1),…

A: Let vertex of Quadrilateral are O(0,0), P(1,-1), Q(3,1) and R(2,4)      Area of the…

Q: 4) Find the centroid of the region that is bounded by the X axis, the Y axis and the line that…

A:

Q: Use cross products to find the area of the triangle in the xy-plane defined by (1,2), (3,4), and…

A:

Q: . Find the centroid of the solid generated by the area bounded by y = sin x and the lines x = 0; x =…

A:

Q: Use Ring Method Rotate the region bounded by x = (y – 3)2 and x = 16 about the x = -5.

A: Let's find.

Q: – 4V5 )ds]

A:

Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

A:

Q: Calculate the volume under the elliptic paraboloid z = 4x² + 6y2 and over the rectangle R = [-2, 2]…

A:

Q: Evaluate this integral Sc v – 2x)dy – (yx – x²)dx where C is a curve consisting of C, which is a…

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Q: 68. Solid bounded above by 3x² + 3y² + z² = 45 and below by the xy-plane

A:

Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: + 1 -оу-х -oy=x2

A:

Q: Find the area and centroid bounded by y^2=-x, x^2+3y+4x+6=0. Graph

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Q: Find the centroid (¯x,¯y)of the region bounded by: y=4x2+7x, y=0,   x=0,   and   x=3 ¯x=    ¯y=

A:

Q: 2. Calculate the centroid of the thin plate R which bounded by r = 1, y = 0 and, 2² + y² = 4.

A:

Q: The area of the region inside the cirde Y = 6 cose and outside the Cardiaid V= 2(1+ Cose) ayo is + 4…

A: Let us consider the curve r=f(θ) The area under the curve is obtained by bounded region is…

Q: 2. The solid bounded by y = 0, x = y², x = 4, and z = Octant (ie. x, Y, z > 0). 2x in the First

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Q: Evaluate the circulation of Gayi + zj+5yk around a square of side 9, centered at the origin, lying…

A: Solution :

Q: Calculate line integral F-dr where F(x, y) = (7x + y, 5x + 2y) and C is a rectangle with vertices 0,…

A:

Q: Find the points on the cone z = x + y that are closest to the point (2, 2, 0)- (x, y, z) = (smaller…

A: Given , z2=x2+y2 and a point (2,2,0) We need to find the closest point Distance formula…

Q: Calculate the volume under the elliptic paraboloid z=3x2+7y2 and over the rectangle R=[−2,2]×[−4,4

A: Explanation: We know that,  Volume =∬zdydx By using the double integral concept, the volume of the…

Q: Find symmetric equations of the normal line to the surface 3xy-z = 0 at the point (-4, -2, 24). O…

A:

Q: Find the centroid of the region bounded by a. y = x3 + 3 and the lines x = b. the x-axis and the…

A: The centroid of a region can be calculated using the formula x=1A∫abxf(x) dx, y=1A∫cdyf(y)dy. Here,…

Q: Consider the region in the first quadrant bounded by y=x^2, the y-axis, and y=4. -the y-axis using…

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Q: Use Ring Method Rotate the region bounded by y = x2 – 2x + 4 and y = x + 14 about the x – axis.

A: The given curves are y=x2-2x+4 , y=x+14 and x -axis To find: the volume the region bounded by the…

Q: Evaluate the lino integral y+ + (4+2-x>y +2が Where C consitts of line segments from 0,-,2) to…

A: