Verify Green's Theorem by evaluating both integrals ам | y2 dx + x2 dy dA ду for the given path. C: rectangle with vertices (0, 0), (8, 0), (8, 9), and (0, 9) | v² dx + x² dy aN dA = ax ду

Q: Find [r(t) u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = cos ti + sin tj + tk, u(t) =…

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Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy = -72

A: To evaluate: ∫02∫-72y2∫-48zyz dx dz dy

Q: Find the area of the region enclosed by the curves y = x² and y integrating with respect to y. = 6x…

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Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2

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Q: A torus is formed by revolving the region bounded by the circle x² + y² = 9 about the line x = 5…

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Q: Evaluate (2x – y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 9

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Q: Evaluate the definite integral. 9ti +3t'j + Vtk) dt

A: The given integral,          ∫-119t i+3t3 j+t3kdt

Q: Find the volume of the solid that results when the shaded region is 8 revolved about the indicated…

A: Volume of revolution

Q: Use a triple integral to find the volume of the solid in the first octant bounded by the coordinate…

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Q: Question 3 Express the area of the given surface as an iterated double integral, and then find the…

A: Let's find.

Q: Use a triple integral to find the volume of the solid. The solid bounded by the surface y = x and…

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Q: Find the area of the region(s) enclosed by the curve y = |2x - 6|, the x-axis, and the lines x = 0…

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Q: Evaluate the vector-valued function at each given value of t. (If an answer does not exist, enter…

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Q: for the given path. C: x = 2 cos(8), y = sin(@), o se s 27

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Q: Express the area of the given surface as an iterated double integral, and then find the surface…

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Q: r = V cos 20 r = 5 cos 0

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Q: Jse a double integral to find the volume under the plane z = 38x + yand over the rectangle R = {(x,…

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Q: Find r(t) for the given conditions. r"(t) = -4 cos(t)j – 3 sin(t)k, r'(0) = 3k, r(0) = 4j %3D %3D…

A: Given

Q: Evaluate the triple integral. xy sin(yz) dV, where G is the rectangular box defined by the…

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Q: Given the following functions: f(x) = cos(x) g(x) = x + 1 Find f(g(x)) and 8(S(x). (Use symbolic…

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Q: Question 14 1. 2 Evaluate the iterated integral. J, J. J. (x²+ y² + z?) dx dy dz -1°0 (А) 5 (в) з D)…

A: To find following integral valueI=∫-11∫02∫01(x2+y2+z2)dx.dy.dz

Q: Use a double integral to find the volume under the plane z = 22x + yand over the rectangle R = {(x,…

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Q: Find the unit tangent vector to the curve at the specified value of the parameten r(t) = 4 cos(t)i +…

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Q: Question 9 1/2 Evaluate the iterated integrals J. J. sine r cos e dr de A 1/6 B) 1/2 6 D) 11/9

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Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: Find the directional derivative of the function at P in the direction of v. g(x, y) = V x2 + y2,…

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Determine the work done by the constant force. The locomotive of a freight train pulls its cars with…

A: Given data÷

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -180 J-120

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Q: 324-y' y dx dy 18

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Q: Find T(t) and N(t) at the given point. r(t) = 3 cos(t)i + 3 sin(t)j + tk; t= 2

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Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t) =…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 51…

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Q: 1009 1010 Suppose R= E (2k) = 2 + 4 +6+.+2018 and S= D (2k-1) =1+3+ 5+.. + 2019 What is the value of…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 4 cos(t)i…

A: To find unit tangent vector at given parameter.

Q: NC2)=

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Q: n-1 1. b) Determine whether the series is convergent or divergent. If it's convergent, 4" n=1 find…

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Q: Use Green's Theorem to evaluate the line integral. y² dx + xy C: boundary of the region lying…

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Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: Use a triple integral to find the volume of the solid in the firsy octant bounded by the coordinate…

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Q: Evaluate J xy dA¸ where Ris the region in y =x? 2 A 13/7 16/3 18 D) 20 B.

A: To find : ∬xydA where  R is the region of y=x2 and y=0

Q: -6w + x + 3y + 6z = -6 -7w - x – 9y – 2z = -33 -4w – 9x + 8y + 9z = -94 -w – 6x – 10y + 9z = -202…

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Q: Use spherical coordinates to find the volume of the solid. The solid enclosed by the sphere X y² +…

A: We have to find the volume of the solid.

Q: Find V x (V × F) if F(x, y, z) = 6xyj+7xyzk. V × (V × F)

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Q: Find the centroid of the region. NOTE: Enter the exact answers. (ë, g) = | (?,?) y = z

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Q: Determine the area of the region bounded by y=2x^2+10 and y = 4x+16

A: To find the area of the region bounded by the given curves.

Q: Determine the volume of the solid obtained by roteting the region bounded by y=x^2-2 and y=x about…

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Q: What is the closed-form expression for the series 2 (k+ 1)², k=1 13 n3 + B

A: First expand the squre  term and make it in standard format then use the formula of summation.

Q: The position vector r describes the path of an object moving in the xy-plane. Position Vector Point…

A: Given :r(t)=6costi+6sintj

Q: Evaluate the iterated integral. NOTE: Enter the exact answer. yz dx dz dy -162 -108

A: ∫02∫-162y2∫-108zyz dx dz dy∫-108zyz dx=(xyz)-108z…