Calculate the double integral of f(æ, y) over the triangle indicated in the following figure: 4. f(x, y) = 12ye" i 23 4 5 Answer : 6(e^3-1)

Q: Express the triple integral in cylindrical coordinates. '5 25 - x2 f(x, y, z) dz dy dx 25 - x2

A: x=r.cos(θ) y=r.sin(θ) z=z where r=radius              θ=azimuthal angle             z=height

Q: Evaluate the integral by reversing the order of integration. V3n V3 cos(4x2) dx dy

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Q: Calculate the double integral. 6x/1+xy dA, R=[0,6]x[0,1]

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Q: 5. Verify Green's Theorem for 0(xy +x )dx+(4x-1) dy where Cis shown below by (a) computing the line…

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Q: m,neIN ce2 (MTIX) Cos(NTTY) dxdy

A: ∫01∫01xy cosmπxcosnπydxdy=∫01x cosmπx dx∫01y cosnπy dy

Q: Use symmetry to evaluate the double integral. Ja+ (1 + x8 sin(y) + y sin(x)) dA, R= [-π, π] x [-π,…

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Q: dz Z 1. around unit circle of radius 1 and center at (0, 0) counterclockwise. 2. By using direct…

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Q: Compute The double integral of a function f(x, y) = 73 over a rectangle [2, 4] × [3, 6]

A: To compute the double integral of a function fx,y=73 over a rectangle 2,4×3,6

Q: What change of variables is suggested by an integral containing Vx? + 36?

A: For, an integral containing  x2+36 we can change variable by substituting, x=6tanθ, As it will get…

Q: Sketch the domain of integration and express it as an iterated integral in the opposite order given…

A: Given that, ∫04∫x4fx,ydydx So domain is, x=0, x=4y=x, y=4

Q: Evaluate the double integral : dy dz

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Q: What is §3dx, §5du and §e^u dt? Those are integrals

A: a) We factor out 3, then integrate. c=integrating constant

Q: Set up an iterated triple integral equal to | = √√3 √3-x² √√30 x²+y² 3 √2-√4-x²-y² 2y dz dy dx…

A: The given problem is to set the given triple integral in Cartesian coordinates to convert into the…

Q: I| ( xy² + y dA, R={(x, y)|2 < x < 3, –1< y< 0} R

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Q: Find the center of mass and the moment of inertia about the​ y-axis for a thin rectangular plate cut…

A: Given that density = x + 2y + 4 and rectangular plate is bounded by the lines y =1 and x = 6

Q: Set up an iterated triple integral equal to √√3 S√ SO 3-x² x²+y² 3 2- 4-x²-y² using: a. Cylindrical…

A: Since you have posted multiple questions, we will solve the first question for you. If you want any…

Q: Evaluate the integral by changing to cylindrical coordina xz dz dx dy -2J-/4-y² x+y²

A: Introduction:   Let f(x,y,z) be a three-variable continuous function defined over a solid Q. The…

Q: Find the complete integral of (1 az 1 dz z dx2 1 az Exe z dx3 z dx *Ex 7x Ix =|

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Q: Evaluate the integrals in Exercises using integration by parts.

A: Integration of a function is the process of finding the anti-derivative of the function. The…

Q: thi.2 Evatuate the foltawingcartesian integrats by changing them inte equivalent Pelar integrals: 2.…

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Q: Please solve in steps. And highlight main equations.

A: The given curve is: σ(t)=sin(t) cos(t), 3t2, et

Q: 9. i Convert S²₁ 4²(4-4x² - y²) dydr into a triple integral with dV = dydzdz.

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Q: Sketch the region of integration. "In 10 r10 1 dy dx In y

A: As y varies from y = ex to y = 10 , we see that x varies from x = 0 to x = ln 10

Q: x2 b) dx Væ³ + 1

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Q: sketch, reverse and evaluate the integral dy dz 15

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Q: What is the integral of the constant function f(x, y) = 5 over the rectangle [-2, 3] x [2, 4]?

A: Given:            f(x, y) = 5   over rectangle -2, 3×2, 4

Q: Calculate the double integral. 7x sin(x + y) da, R = [0, * [0, =]

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Q: Evaluate the double integral: dy dr

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Q: z+6 dz Evaluate the integral using integration by parts technique :

A: We have to evaluate the integral by parts technique∫03xx+63dx.

Q: The amount of work that a force field does on a particle as it moves along the boundary of a…

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Q: S. (3x² – 3yz + 2xz)dx + (3y² – 3xz + z?)dy + (3z² – 3xy + x² + 2yz)dz

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Q: Evaluate the line integral ∫(AB) xdx+ydy+zdz using the fact that the integrand is a perfect…

A: Here we find ∫(AB) xdx+ydy+zdz,   by using the fact that the integrand is a perfect differential. A…

Q: sketch, reverse the order of integration then evaluate 2. d xely Iny

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Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: rcos (y) dA, R= [-2, 3] × [0, ]. Evaluate R

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Q: Evaluate the iterated integral by choosing the order of integration. 4 In(y) + dy dx /1 2y + 1

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Q: Evaluate be (x² + y²) ds, C is the right half of the circle with radius 3 centered at (0,0). Hint:…

A: To evaluate    ∫Cx2+y2ds where C is the right half of the circle with radius 3 centered at 0, 0.…

Q: Calculate the double integral. SSR 6x / 1+xy dA, R = [0, 6] × [0, 1]

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Q: Integrate f(z) = 1 counterclockwise around the unit circle, using 28 – 4.4 Cauchy's integral theorem…

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Q: Calculate the double integral. Te 1+ xy бх dA, R = [0, 6] × [0, 1] 1 + xy

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Q: Vx 3+4x+8 dx 2 vã (Vx?)

A: The given function is x34+4x+8xx23 We have to identify u and du and the form of the integral of this…

Q: Evaluate the integral by reversing the order of integration.

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Q: EVALUATE THE FOLLOWNG DOUBLE INTEGRAL BY REVERSING THE ORDER OF INTEGRATIC Vx²+! 'dx dy

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Q: b) Calculate the line integral of F along the boundary of the rectangle [0, 1 x[-1, 2], traversed…

A: According to the given information, consider the vector field. It is required to calculate the line…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. Lv - x) dx +…

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Q: Evaluate the triple integral,   4x dV, where E is bounded by the paraboloid x = 5y2 + 5z2 and…

A: To calculate the value of the triple integral under the given terms

Q: . The work required to move a mass m "infinitely far" from a planet of radius R and mass M is given…

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Q: Determine by direct integration the moment of inertia of the shaded area with respect to the x axis.

A: From the given graph, The function y = k x13  limits from x = a  to  x = b

Q: (2 - I) 4) Calculate Ahe integral se dz

A: As we know that; The Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And The Sum Rule: ∫fx±gxdx=∫fxdx±∫gxdx From…