Prove that the kronecker delta and Levi Civita Tensox of respectiely. Symbels 2 and are rank 3.

Q: consider surface S with paramirization Glusv) = cu. Vo uv) ノ surface of s areu also compute the

A: Differentiate Gu,v=u,v,uv with respect to u and v, to find Gu and Gv, and then compute Gu×Gv.…

Q: Sketch the region whose area is represented by the iterated integral. dyds un

A: Option C is correct.As lower limit in inner integration is tanx2 which you can see in the graph.if…

Q: calculate th integral SSo(x+y) dydx where D is th reigon that deter mined in thees Curves : Y = x, Y…

A: Solution is given below:

Q: Find the volume of the solid bounded by the graphs of r = 3 sin 30, : = 4 + Vx2 + v², = = 0, in the…

A: First, plot the graphs of the given functions. Then, identify the limits.

Q: Evaluate SII xdv, where Dis the region bounded by x-yz-0, X=0, 2•0, and yol. y=x+2 (back)

A:

Q: By using the de finition of intepral, show that

A: First integrate LHS with respect to x and then put the limits.

Q: Use integration by parts to evaluate the integral: fin(z) · Vz"dz = 19 + C

A:

Q: Find the volume bounded by z = 9-x²-y² and z = 0.

A: find explanation below

Q: And the Volume of the sond generated by revoluing the vegion bounded by the qiven limes f'aurves…

A:

Q: Find the volume of the solid bounded by z = 4х - Зу, Зу %3D 4х, Зу %3D - 4х and x = 7. Leave your…

A: Given that z = 4x - 3y, 3y = 4x, 3y = - 4x and x = 7 We have to find volume.

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: Suppose that f (x, y) satisfies f(-x,y) = –f(x, y). Give an /| s(x, y) dA = 0. example of a region D…

A: As per our guidelines we are supposed to answer only One question if there are multiple questions…

Q: Find the volume of the colid obtained by rotating about th bounded by y=2x² axu the region and yo

A: First we plot the curves and identify the region which is to be revolved about y-axis. at…

Q: Integrate the Runction. over the region boundeal by y-x ,ye6x, yoo

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Q: how by integration that the centroid of a uniform semi-circular lamina of radius a from ne centre is…

A:

Q: 2. bounded by the axis of the region Volume of the body of rotation created by rotating it Oround ?

A: Given that  y = 1 -x2, x =0 , y = 0   x2 = 1- y The limits of y :-  from y = 0 to y = 1

Q: Iff is Riemannintegrable fuction, then prove the following If is Riemannintegrable @fis Riemann…

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

A: Given

Q: Find the volume V under the the plane z = 8x + 6y over the region R = (x, y) : 0 ≤ x ≤ 1, 0 ≤ y ≤…

A: We have to find the volume under the plane z=8x+6y over the region R=x,y:0≤x≤1,0≤y≤2x2 (a) Draw the…

Q: Consider the lamina that occupies the triangular region with vertices (0, 0), (2, 2) and (2, –2),…

A: Given, the lamina that occupies the triangular region with vertices (0, 0), (2, 2) and (2, -2), with…

Q: Flxyy) de dy is an integral orer what region?

A:

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

A:

Q: 9. The Theorem of Pappus will always be applicable to determine the volume of solid revolution for…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Find the volume of the solid in the first octant bounded by the coordinate planes and the passing…

A: Given- 1,0,00,2,0 and 0,0,3 To find- The volume of the solid in the first octant bounded by the…

Q: please prove this using the definiton of compactness

A: To show that the given set 1n|n=1,2,3,.....∪0 is compact.

Q: Evaluate the integral hipxp hx^ 7 and the hyperbola ry = 13. where R is the region bounded by the…

A:

Q: Calculus 4

A: The given double integral is

Q: The figure shows a steel semi-circular plate described by a region D. Assume a constant (uniform)…

A: Here is the Answer and Explanation

Q: as Find Hhe voleime of odid generated by revolving tthe region bounded by graphs of y=xe;y 0, and…

A:

Q: Find the volume of the solid generated by revolving the area bounded by x2 – 2kx – 4ky + k2 = 0 and…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 8. Find the volume generated when the plane area bounded by y=-x²-3x + 6 and x + y - 3 = 0 is…

A: Finding the volume generated by revolving along x and y axis

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

A: Given that, y = x2 ; x = 0; y = 15 3) Volume of the region bounded by the given curve rotated about…

Q: Sketch the region which is defined by the given condtions. 0 ≤ θ ≤ π, r ≤ 3

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Q: 4 Set upinbegrl for th volume caboud x- -I y. 12 and

A: Volume problem.....

Q: A region R is bounded by the graphs of y=0.5 Vx and y=0.5x. Find the moments Mx and My of R about…

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Q: If a region have axes of symmetry at y = x and y = -x then its centroid is at the origin. True O…

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Q: Exercise 6. Evaluate the integral ffn ldA, where D is the region bounded by the lines y = 2x + 5, y…

A: Let us considre the given integral I=∫R∫f(x,y)dxdy Transform the variable to x=f(u,v)y=g(u,v) The…

Q: Consider a region bounded by the graphs of y = x4 and y = x5. Show that the center of mass lies…

A: It is given that the density of the plate is  and the region bounded by the graphs of y = x4 and y =…

Q: Find the Center of Mass of Lamina bounded bythe graphs

A: We have to find out the center of mass of given lamina bounded by x=y2,x=1 and ρ(x,y)=y2+x+1.

Q: Let ECR³ be the region in the first octant bounded by z = 1 - y² and 2 = 1 x². Determine SSS 2x dV.

A: Given the region bounded in the first octant bounded by z=1-y2 and z=1-x2

Q: Use three-particle interaction to show that mass is an additive.

A: We have to use three-particle interaction to show that mass is an additive.

Q: Let C be a simple closed curve bounding a region Din R2. which of the following are equal to the…

A: Let C be a simple closed curve bounding the region D in R2.  So using Green's-Theorem,

Q: 4 SET UP AN INTEGIUL fonila fen SUifACE Arfer BounDED By Y=x-2y, x-C , Y=3, Auo x 20 CHEN ReTATowh…

A: The integral for finding surface area of the solid obtained when the region rotated about y axis is…

Q: 3. Find the volume of the tetrahedron in the first octant bounded by the coordinate planes and the…

A: Given

Q: Use Simpson's Rule to estimate the centroid of the region shown. yA 4 2 6 8 x 4.

A: The number of subintervals as n=8. Calculate the subintervals ∆x of the region:  ∆x=b-an…

Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

A:

Q: Find the centroid of the volume generated by revolving about the line X=1, the area bounded by

A: The required region is as shown below:

Q: If, in an integral triple, we have a D region bounded by the surfaces z = 2x² - y² and z = 9 - 2x² +…

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Q: *Sketch all appropriate regions or solids." Evaluate the integral [[2y² cos(xy) dydx.

A:

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

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