(i) Evaluate the double integral (x + y) dxdy where D is the triangular region in the xy plane with vertices (0,0), (3,0) and (2,1).

Q: (2y – x*)dx + (4x + y²)dy where C is the boundary of the region in first quadrant bounded by x2 – 2x…

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Q: Evaluate the double integral. I| 2y2 dA, D is the triangular region with vertices (0, 1), (1, 2),…

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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: d the volume V of the solid obtained by rotating the region bounded by the ren curves about the…

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Q: 7. Evaluate the double integral S2 (x sin(y) – y sin(x)) dA over the rectangular region R= {(x, y) :…

A: We have to evaluate the double integral ∫∫Rxsiny-ysinxdA over the rectangular region…

Q: 15. Evaluate the double integral (a + 6y? + bx²y) dA, where R = {(x, y) E R² : |x| + \y| < 1}.

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Q: Use Green's Theorem to evaluate the line integral. | (x - 4y) dx + (x + y) dy C: boundary of the…

A: The given integral is ∫Cx-4y dx+ x+y dy,  where C is the region bounded by x2+y2=1 and  x2+y2=16 To…

Q: Evaluate the double integral. dA, D = {(x, y) | 0< x < 8, 0 < ys Vx} %3D

A: The given integral is ∫∫Dyx2+1dA, D=x,y|0≤x≤8,0≤y≤x. Evaluate the given integral as follows.…

Q: Evaluate the triple integral. SSSE2.xy dV , where E lies under the plane : = 1+x + y and above the…

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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: Sketch in the xy-plane the region of integration for the integral /6 (cos 20 g(r, 0)r dr de. w/6…

A: Given Data The integral is ꭍ-π/6 π/6 ꭍ1/2 cos 2θ g(r,θ)rdrdθ.   The sketch of the region of…

Q: - Evaluate the double integral / (x+2y)dA, where D is the region bounded by the parabolas y = 2x2…

A: Consider the parabola, y=2x2,    y=1+x2 To sketch the region of integration,

Q: I| (12y – 8x) dV where E is the region bounded by y = 10 – 2z and in front of the regic bounded by z…

A: Please refer to the image below.

Q: Evaluate the double integral ∫∫R  y / (1 +xy)2 dA, where R= [0,1]×[0,1].

A: Given integral is  where  R= [0,1]×[0,1].

Q: Evaluate the double integral [[R E¬Y°DA where R is the triangular region in R² with vertices (0,0),…

A: – “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Use Green's Theorem to evaluate the integral In(x2 + 1)dx – xdy, C is the boundary of the region…

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Q: Evaluate the triple integral. II (x - y) dV, where E is enclosed by the surfaces z = x2 - 1, z = 1 -…

A: Calculate the points of intersection of the curves, x2-1=1-x22x2=2x2=1x=-1,1 According to the…

Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 <ys 2, y – 1 < x< 1}

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Q: Eval u ate the double integrals overs the indicated re sions り ye JA, R: the region bonnded by the…

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Q: Evaluate the integral of the two-form w = (x8 + 2y) dx A dy over the region D bounded by the curves…

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Q: Evaluate the double integral / |: xy dA where D is the region bounded by the line y = x – 1 and the…

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Q: Evaluate the double integral integral integral_(D) e^(−y^2) dA, {R = (x, y) | 0 ≤ y ≤ 3 , 0 ≤ x ≤…

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = E : 6y² + 6z²…

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Q: Suppose that f(x, y) 4 - a? - y and D = {(x, y) | 2² + y² < 4}. Then the double integral of f(x, y)…

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Q: 5. Evaluate the double integral (a + 3x + bry) dA, where R= {(x, y) E R² : |x|+ |y| 0 and b > 0).

A: To Evaluate: ∬Ra+3x2+bxydA, whereR=x,y∈ℝ2:x+y≤1

Q: 3) Evaluate the double integral fS, dr dy where D is the region bounded by the hyperbolas ry = 2, ry…

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Q: valuate the double integral. (x2 + 2y) dA, D is bounded by y = x, y = x³, x 2 0

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Q: Q3 Verify Green's theorem in plane for (x² - 2xy) dx + (x²y + 3)dy where c is the boundary of the…

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Q: Calculate the double integral. ∫∫ x sec2y dA, R = {(x,y)| 0≤ x ≤2, 0≤ y ≤ π/4 }

A: Given: The given function is  f(x,y)=x sec2(y) and the region is R=(x,y)|0≤x≤2 , 0≤y≤π4  To find: we…

Q: Suppose that f(r, y) = /4 - a? – y? at which {(x, y) | 2² + y² < 4}. Then the double integral of…

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Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Final answer is 65/84.

Q: set up the double integral for the area of the portion of the paraboloid z=x^2+y^2 that is between…

A: z=x2+y2∂z∂x=2x∂z∂y=2y

Q: Evaluate the double integral 4.x dydr 9 + y2 I when A is the shaded region in enclosed by the graphs…

A: Evaluate the double integral.

Q: c9-x² f(x, y) dy dx as an iterated integral in the Express order dx dy.

A: ∫-33∫09-x2f(x,y)dy dx

Q: Evaluate the double integral (x-5 y) dA es A(0,0), B(2,-1), C(3, 0). Draw the region D.

A: Draw the given points A(0,0), B(2,-1), C(3,0) in the xy-plane.

Q: Evaluate  DOUBLE integral xy dA, where D is the region bounded by the line  y = x − 1 and the…

A: Given: The bounded regions are, Find the points where the bounded regions intersect. Substitute…

Q: Evaluate the double integral. y dA, x2 + 1 D = {(x, y) | 0 s x< 6, 0 s y s Vx}

A: Answer and explanation is given below

Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

Q: 3. Evaluate the triple integral where E is the region behind y = 10 – 2z and in front of the region…

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Q: Q2/(a): Evaluate the double integral , 3xy dA over the rectangle dA = dydx} R {(x, y): -3 x< 2,…

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Q: Evaluate the triple integral x dV where G is the solid that lies below the surface z = 15xy and G.…

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Q: 4. Evaluate the double integral x cos y dA; R is the triangular region bounded by the lines y = x, y…

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Q: Calculate the (x - 3y)dA R integral by making x=2u+v and y=u+2v conversions, including the…

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the…

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Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

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: Realize Crane's theorem for linear integration (e* + y²)dx + (ey + x²)dy where c is the region…

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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.

Q: Evaluate the line integral [2y'dx+(x* +6y°x)dy where C is the boundary of the R region shown below…

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