21 Verify that (y² – 2x )dx +(2xy +x²)dy = || dA where C is the boundary of a region ôy -. R R defined by y = 0, x = 1, and y = x².

Q: Verify Green's Theorem by evaluating both integrals dk + x° dy = /. / dA ду for the given path. C:…

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Q: (b) / = xyz dV if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: 4. Find the centroid of the region bounded by graphs of y = 4x – x², y = 2, and r = 0.

A: As per guidelines we experts are allowed to solve one problem at a time. Please reupload the fifth…

Q: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: Verify Green's Theorem by evaluating both integrals y² dx + x² dy = / dA дх ду for the given path.…

A: Here we have to verify the Green's theorem.

Q: (b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y…

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Q: 2 Evaluate 2 dA where D is the region described by 0s ys 55 - x Integral is equal to : Enter an…

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Q: Verify Green's Theorem by evaluating both integrals aN dx + x² dy = / / dA ay y2 ax for the given…

A: To verify green's theorem by evaluating both the integrals.

Q: (i) Evaluate the double integral (x + y) dxdy where D is the triangular region in the xy plane with…

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Q: Hw.3 3 Find the areas for the following Vegions: Region boundded by y=x y , and Region bounded by…

A: To find the area of the following region :-

Q: Use Green's Theorem to evaluate the line integral Scox (y - x) dx + (2x - y) dy for the given path.…

A: The given integral is                                    ∫Cy-xdx+(2x-y)dy for the given path.…

Q: (c) By using the Green's theorem, evaluate $(2xy) dx + (4x²y*) dy if C is the boundary of a region…

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Q: Use Green's Theorem to evaluate the line integral (y - x) dx + (2x – y) dy for the given path. C:…

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Q: Use Green's Theorem to evaluate the integral (v-x) dx + (2x−y)dy for the path C. boundary of the…

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Q: Q1 Verify that [Oy²-2x )dx +(2xy +x² xdy = [[ ƏP dA where C is the boundary of a region R R defined…

A: We have to verify ∫Cy2−2xdx+2xy+x2dy=∬R∂Q∂x−∂P∂ydA, where C is the boundary of a region R defined by…

Q: Let C be the boundary of the region x² + y² < 1 and (x + y)² < 1 which is oriented counter-clockwise…

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Q: 9. Use Green's Theorem to evaluate (e* +y²) dx +(e" +x²) dy where C is the boundary of the region…

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Q: 6. Compute the integral zez²+y²+z² x2 + y? + z2 dV(x,y, z) over the region P = {(x, Y, z) ; x² + y²…

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Q: Evaluate: ∬ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2.

A: Plotting the Curves on X and Y-axis : y = x2 ...............(1)y = x + 2 ..............(2)After…

Q: 3. Use Green's Theorem to evaluate (e3x +y²)dx + (sin y – x²)dy where C is the boundary of the…

A: Green's theorem

Q: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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Q: 4. Evaluate fe cosy dx + (xy – xsiny) dy where C is the boundary of the region lying between the…

A: Given  ∫Ccosydx+(xy-xsiny)dy

Q: Use Green's Theorem to evaluate f x2 dx+ (xy+y²) dy where C is the boundary of the region R bounded…

A: follow next step

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: 1) Evaluate the triple integral. | 6xy 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 (y – x) dx + (2x – y) dy for the given path. = x²…

A: Green's Theorem: By Green's Theorem we have for a differentiable function f(x,y)=M(x,y)+N(x,y) and a…

Q: 1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the…

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Q: Verify Green's Theorem by evaluating both integrals aN y2 dx + x2 dy dA ду - əx for the given path.…

A: For c-1 sign is negative because of opposite direction

Q: 1) Find the centroid of the region that is bounded by the line Y = 3X, the line X = 2 and the X…

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Q: Verify Green's Theorem by evaluating both integrals y2 dx + x2 dy = dA ду ax for the given path. C:…

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Q: The double integral R f(x, y) dA over the region R = {(x, y)| - 2< x < 2, x - 8 < y< -x²} can be…

A: Given integral is ∬Rfx,ydA over the region  R=-2≤x≤2x2-8≤y≤-x2 The limits and order of the…

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: 2. Evaluate [(3yz)dV where B is the region in the first octant lying below the plane x + 2y +2: = 4.

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Q: Use Green's Theorem to evaluate the line integral √(x − x) dx + (2x - y) dy (y- for the given path.…

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Q: SSR (r + y)2 dA, where R is the region bounded by the limaçon r = 2 + cos 0

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Q: Use Green's Theorem to evaluate (eš + y³)dx + (sin y – x²)dy where C is the boundary of the region…

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Q: Let R be the region in the half plane x 20 bounded by the curves y = -5x + 5 y = x2 – 1 x = 0…

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Q: b.) xyz dv if S is the region bounded by the cylinders x² + y² = 25, x² + z² = 25 and the first…

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Q: (a) Calculate the centroid (7, y) of the region under the graph y = cos x for 0 < x <T/2.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Sketch the region R and evaluate the iterated integral ff- (1-4x+6y) dy dx y -1.0 O -0.5 3 -1 xn-[…

A: The given integral is  ∫01∫02(1-4x+6y) dy dx re write the integral: ∫01∫02(1-4x+6y) dy dx =∫01…

Q: Verify that [y- 2x )dx +(2xy +x²)dy = dA where C is the boundary of a region %3D R R defined by y=0,…

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Q: O R is the region bounded by y = 2 – x² and y = x² – 6. - %3D

A: 5.)  y=2-x2  and  y=x2-6 red line y=2-x2 blue line y=x2-6

Q: Consider the integral x³+1 x³(x²+1) -dx What is the correct partial fractio OA Bx + C

A: We have to choose the correct option from the given options according to the given information

Q: 4. Compute the value of the double integral fSRe-xydxdy, where R is the region bounded by the lines…

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Q: 17. 6xy dV, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded…

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Q: 3. Use Greens theorem to evaluate (e* + y²)dx + (e' + x²) dy where c is the boundary of the region…

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Q: Use Green's Theorem to evaluate (e" + y²) dx+ (e" +x²) dy where C is the boundary of the region…

A: we have to evaluate the following by using greens theorem

Q: Verify Green's Theorem by evaluating both integrals aN | y2 dx + x² dy dA ax for the given path. C:…

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Q: Evaluate // (1+x² + y2) dV, where E is the region bounded E by the surfaces z = 6y2 - 9x², and z = 6…

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Q: Verify Green's theorem in a plane | (xy +x²)dx + x² dy, where C is the boundary of the region formed…

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