(b) Verify Green's theorem for |(x² – 2x y)d x+(x² y+3)d y, around the boundary e of the region y =8x and x=2.

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

A:

Q: Evaluate p (x² – 2xy)dx + (x²y +3)dy around the boundary of the region defined by y? = 8x and x = 2…

A: To evaluate : ∮x2-2xy dx+x2y+3 dy around the boundary of the region defined by y2=8x and x=2 (a)…

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: (a) Consider the region bounded by the graphs of y=c(2x-4), x-1, x-3. and y 0 where c is just a…

A:

Q: The double integral 2xy³dA over the rectangular region R {(x, y) E R“, 0 < xS 4 and – 1 S y< 0} is…

A: The double integral ∬Rfx, ydA can be written as ∬Rfx, ydxdy. We have given the rectangular region as…

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

A:

Q: Evaluate E=∭D(x2+y2+z2)−3/2dV where D is the region bounded by the surfaces x2+y2+z2=9 and…

A:

Q: Volumes of solids Find the volume of the following solids.

A: The region is bounded by the curves, The region is shown in the graph given below,

Q: 1. Find the area of the surface z = k + xy inside the cylinder x² + y² = R² for constant R. k > 0 is…

A:

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

A:

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

A:

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: integrate ƒ over the given region. ƒ(x, y) = x2 + y2 over the triangular region with vertices (0,…

A: Given: f(x,y)=x2+y2 over the triangular region with vertices (0,0), (1,0),(0,1)

Q: Let R be the region in the half plane x 2 0 bounded by the curves y=-5x + 5 y = x2 - 1 *= 0 Compute…

A: Solution

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: Find the absolute maximum and minimum values of f(x,y)=x2+y2-2y+1 on the region R={(x,y)|x2 + y 2…

A: Given function is fx,y=x2+y2−2y+1 and region is R=x,y|x2+y2≤4. We have to find the absolute maximum…

Q: 3. Suppose the following bounded region is rotated about the x-axis and creates a solid of…

A:

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: 2. Find the area of the plane region bounded by y = 3x + 1, x = 1, x = 3,and the x-axis. y y = 3x +…

A:

Q: 3. A) Evaluate the triple integral xdV, where E is the solid region bounded by the cylinder 4 = y =…

A: 3.A) The given integral is      ∫∫∫E x dV , E is the solid bounded by x2+y2=4, z=0, y=3z, x=0 and in…

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

A:

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

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: Use Green's Theorem to evaluate the integral [(y-x) dx + (2x−y)dy where C is the boundary of the…

A:

Q: 2- Find D xyz dV where D is the region with -1 ≤x≤1, x ≤ y ≤ 1, above z = x, and below z = y + 2.

A:

Q: Find the area of the region described in the following exercise a. The region bounded by y=4x+4,…

A: Since you have asked multiple questions in a single request, we would be answering only first…

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: Calculate an integral ∬R √ (x2 + y2)dA, where R is the region within the upper semicircle of radius…

A:

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

A:

Q: Find the maximum and minimum of w(x, z) = 2xz + z^2 +1 in a region R bounded by x = 0, z = 0, and x…

A: The bounded region R is:

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

A:

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

A:

Q: 21 Verify that (y² – 2x )dx +(2xy +x²)dy = || dA where C is the boundary of a region ôy -. R R…

A:

Q: 1 Find the centroid of the area bounded by x2- 4y + 8 = 0, the lines x = 0 and x = 4, and the…

A: Formulas are written within the solution.

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

A: Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   Given: I=∫Cy-xdx+2x-ydy and C: y=x and y=x2-2x It means…

Q: The double integral ſſ 2xy³dA over the rectangular region R = {(x, y) E R², 0<x<4 and– 1<y<0}is…

A:

Q: e-(z²+y²+z²) dV. x² + y² + z² where E is the region bounded by the spheres x? + y² + z² 1 and x? +…

A:

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: The double integral ff 2xy³dA over the rectangular region R = {(x, y) E R², 0<x<4 and–1<y<0}is equal…

A: Given that, I=∬2xy3dA and  0≤x ≤4  and  -1≤y≤0 here dA = dxdy

Q: The numerical value of л за 3dA (where D is the region bounded by lines y=0 and x = 1, D and the…

A:

Q: The double integral ſſ 2xy³dA over the rectangular region R = {(x, y) E R“, 0< xS 4 and – 1< y< 0}is…

A: Dr

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

A:

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

A:

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:…

A:

Q: b) Evaluate [[ (3-4x)dV where E is the region below :=4-xy and above the region in the xy -plane…

A: