Let D be a planar region and let 4 y/2 6/2 2 || g(x,y) dA = { g(x.y)dx dy + g(x,y)dx} dy D 2 4 y/ 36 / 36 Express the double integral as an iterated integral with the order of integration reversed. b w || g(x,y) dA = J{| g(x,y) dy dx, then D a b = V = and w= a =

Q: Y – 5x |dA 100 cos x + y

A: We have to evaluate the double integral ∬100cosy-5xx+ydxdy over the region D where the region D is a…

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Q: Evaluate the line integral I of the one-form w = (y+ z) dx + (x + z) dy + 10z dz over the line…

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Q: Use the Fundamental Theorem of Line Integrals to evaluate F. dR where x 1 (−2x + 1)²³ y +1 and C is…

A: Given: F→x,y=lny+1-1-2x+12, xy+1+1y2+1 C is the portion of the parabola y=-x2+1 from 1,0 to 0,1.…

Q: Verify Green's Theorem by evaluating both integrals an am dA ax ay for the given path. C: rectangle…

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Q: Integrate G(x,y,z)=z-x over the portion of the graph of z=x+3y² that lies above the triangle in the…

A: Given that G  x, y, z  = z - x              The portion of the graph a curve z = x + 3y2 above…

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

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Q: Evaluate the integral of the two-form w = (a* + 4y) dx A dy over the region D bounded by the curves…

A: Solution:-

Q: Integrate G(x,y,z)=z-x over the portion of the graph of z=x+3y² that lies above the triangle in the…

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Q: Evaluate the double integral I = = //₁₂ xy dA where D is the triangular region with vertices (0, 0),…

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Q: Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

A: Given integral is ∬R (5x + 6y2) dA Where R =  (x, y) | 0≤x≤4, 0≤y≤3

Q: 2. Swap the order of the integral to the order dy dz dz TË Tƒ f (x,y,z) dz dy da

A: Answer

Q: Apply Green's Theorem to evaluate the integral. (4y + x)dx + (y + 3x)dy C: The circle (x-6)² + (y -…

A: We have to find the value of integralFor this we using green theoremThe green theorem says that

Q: Y – 5x |dA x + y 100 cos

A: We have to evaluate the double integral ∬ 100cosy-5xx+ydxdy over the region D where D is the…

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve. 5y +…

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Q: Evaluate the iterated integral.

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Q: x2-2xy a²+y? dy If the ODE dx is exact, find an integral F(x, Y) .

A: The given ordinary differential equation is: dydx=x2-2xyx2+y2⇒2xy-x2dx+x2+y2dy=0

Q: Evaluate the triple integral (* + 1y) dV where E is bounded by the parabolic cylinder y = 32² and…

A: We have to find the triple integral  ∫∫∫E(x+y)dVwhere E is bounded by the parabolic cylinder y=3x2…

Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: Let f(x,y)=|x|+sin (2x−3y). If R is the region bounded by the quadrilateral of vertices (0,3),…

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Q: Evaluate the triple integral of f(x,y, z) z(x2 + y? + z²)-3/2 over the part of the ball x² + y² + z²…

A: please  see the next step for solution

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Q: Evaluate the iterated double integral: IM -3 -x-1 e2y³-3y²-12y dy dx + Im VI-T 2y³-3y²-12y dy dx

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Q: 1 = √√√₁₂² xy dA, where D is the triangular region with vertices (0, 0), (6, 0), (0, 1). Evaluate…

A: To Evaluate: I=∬Dxy dA where the D is the triangular region with vertices (0,0), (6,0), and (0,1).

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Q: Harry fills up his Jeep with gasoline and notes that the odometer reading is 23,511.9 miles. The…

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Q: (a) Verify Green's theorem for the line integral f(x−y)dx + (x+y)dy, where C C is the unit square…

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