Evaluate the triple integral. 6xyz dV, where T is the solid tetrahedron with vertices (0, 0,0), (1, 0, 0), (1, 1, 0), and (1, 0, 1)

Q: Which of the follo wing integrals do we obtain if we write the sum I Vx? +y? dx dy + | ?+ y² dx dy…

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Q: Evaluate the double integral I2 = || v?dzdy T where T is a triangle with vertices (-2, 0), (0, 3),…

A: Here we have to evaluate the given double integral where T is a triangle with vertices…

Q: 6. Evaluate the triple integral f, x?yz dV, B = {(x, y, z): - 2 < x<1,0 < y< 3,1<z<5}

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Q: Calculate the double integral || x + y)?e -r dx dy where R is the square with vertices (4, 0), (0,…

A: Given: ∫∫Rx+y2ex2-y2 dx dy where R is the square with vertices 4,0, 0,4, -4,0, 0,-4

Q: 1. Evaluate the triple integral /// e/y dV where E = {(r, y, 2) | 0 < y < 1, y < a < 1, 0<z< ry}.

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Q: e* dx? e* – e -> What is the integrable form of du ? du

A: Explained below

Q: Question 3. Compute the integral dz 8+z where y is the rectangle with vertices +3+i with the…

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Q: 10. Consider the double integral JR 1+x²+y²' ху dxdy. (a) Evaluate the integral where R is the…

A: step:-1 Given integral is ∫∫R xy1+x2+y2dxdy Part (A):-  vertices A1, 0, B5, 0, C7, 3  Now, equation…

Q: Calculate the double integral || (x + y)?ex -ý dx dy where R is the square with vertices (2, 0), (0,…

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Q: 2 (2y-y² a 15. Evaluate the integral / / |zVx² + y²dzdrdy by using cylindirical coordinates. 0 0

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Q: (b) Find the value of the following integrals: z-1 1- dz, y is the triangle with vertices at the…

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Q: Use spherical coordinates.Evaluate the triple integral of (x2 + y2) dV,  where E lies between the…

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Q: 7. Evaluate, in spherical coordinates, the triple integral of f(p,0, 0) = cos 0, over the region 0 <…

A: Answer is 3√3π .

Q: Suppose R is the triangle with vertices (–1,0), (0, 1), and (1,0). (a) As an iterated integral, B //…

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Q: 10. Use Green's Theorem to evaluate the integral fe y dx + 2xy³ dy, where C is the square with…

A: Introduction: By applying Green's theorem, one can determine line integral through surface integral.…

Q: Let E be the pyramid with top vertex at (0,0,1), and base vertices at (0,0,0), (1,0,0), (0,1,0) and…

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Q: Q3(a) Solve the integral below by using polar coor dinate and sketch the region 2-yt 2xy dxdy J-/2-y

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Q: Evaluate the iterated integral. 7 2 z z [ [²] ² 1 -1 J-y Y (-72+3 ln (7)) x dx dz dy

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Q: 4. Solve the triple integral below using spherical coordinates IIT √√√x² + y² +2²dzdydx

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Q: SI. f dV here D is the solid region in the first octant between the elliptic cylinder 4x2 + 22 = 16…

A: Find the limits of x , y,z then compute integral

Q: 3) Evaluate the cylindrical coordinate integrals in: 2n 1 1/2 ISPsin'e + z") dz r dr de e-1/2

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Q: 1- 2- 3- 3-Evaluate the integrals in Exercises: [ sect? (x - 1) dx sech² s sech Vt tanh Vt dt Vt…

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Q: 2. Convert the integral In(r² + y? + 1) dx dy into a polar integral and then evaluate it

A: Explained below

Q: Evaluate the triple integral [ 2³ dV, where E is the solid tetrahedron with vertices (0,0,0),…

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Q: Which of the follo wing integrals do we obtain if we write the sum Jx² + y² dx dy + I I Vx? +y² dx…

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Q: Evaluate the triple integral I = II 3(x2 + y²) dV where D is the region inside the parabolid z = 9 –…

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Q: II EVALUATE THE ITERATED INTEGRAL. dydx 1+ y? tan x 1. eIn y SIT xe'dzdydx 2.

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Q: 11. The y-coordinate of the centroid of the solid in part IV is.. A. 0 В. 1 С. 2 D. 3

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Q: By using Green's theorem, evaluate P(2y)dx+(4x)dy where C is the triangle ABD with the vertices…

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Q: (1) Evaluate the triple integral I zyz dV, R where R = {(z, y, z)| 0 < z < 3, -2 <y< 1, 1< z < 3}.

A: We will use simple Integration rules to solve this triple integral.

Q: Use polar coordinates to evaluate the Gaussian integral -2x2 e dx. 8e-2a2

A: The objective here is to evaluate the given Gaussian integral using polar coordinate. Given Gaussian…

Q: b)I bounded by y 2 0, z 2 0, x > 4z, and 16 > x + y. Evaluate the following triple integral: Let E…

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Q: (b) Find the value of the following integrals: z-1 1- dz, y is the triangle with vertices at the…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Evaluate the iterated integral. 2 3y [ ?+y?) dx dy -1 0 2 3y +y?) dx dy = -1 0 (Type an exact…

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Q: Evaluate II| 6x(x2 + y2) dv, where E is the solid in the first octant that lies beneath the…

A: Since the integral lies in first octant so 0≤θ≤π/2 and z≥0.  Converting into cylindrical coordinates…

Q: #1. Evaluate the triple integral xy*av, xy?dV, B where B is given by B = {(x,y,z): 2 <x< 3, -1< y <…

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Q: #2. Evaluate the triple integral x dV, E where E is given by E = {(x, y,z) : z< x < 2z, 0 < y<x+z,…

A: Solve it

Q: xy dx + x2y3 dy, Cis counterclockwise around the triangle with vertices (0, 0), (1, 0), Jc and (1,…

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Q: Evaluate the double integral 2xy dA, where D is the triangular region with vertices (0, 0), (1, 2),…

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Q: Find the value of the closed loop integral z3 + sin z -dz (z – i)3 taken around the boundary of the…

A: GIven  ∮z3+sinz(z-i)3dz   To compute this integral we have to use the following theorem. Theorem:…

Q: e* What is the integrable form of dx? A du B du du D du

A: Solve by substitute

Q: 15. Use the indicated change of variables to evaluate the double integral ||18xy dA where R is the…

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Q: Verify Green's Theorem by evaluating both integrals y? dx + - x² dy = da ду %3D ax for the given…

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Q: Evaluate the triple integral -3pi D x dV where E is the solid bounded by the paraboloid x = 6y² +…

A: Solution is given below:

Q: Verify Green's Theorem by evaluating both integrals y? dx + x2 dy dA ду for the given path. C:…

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Q: Evaluste the line integral using Green's Theorem and check the answer by evaluating it directly.…

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Q: 4) Using Green's theorem, convert the line integral f(6y² dx + 2xdy) to a double integral, where C…

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Q: 5) Using Green's theorem, convert the line integral f.(6y² dx + 2xdy) to a double integral, where C…

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Q: 2. Set up (Do Not Evaluate) the triple integral /// f(a, y, 2 )dV E for the following regions. a) E…

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Q: Calculate the double integral || (x + y)?e* - Ý dx dy where R is the square with vertices (2, 0),…

A: According to the given information, it is required to find the integral over R where R is square.