B is counterclockwise boundary of the region that is enclosed by the x-axis, the y = x - 2, and the curve y= Vx. Evaluate the equation below using Gre theorem. (x2 – 2y2) dx + (y³ – xy) dy

Q: Q1: Evaluate: 2x dV where E is the region under the plane 2x + 3y + z = 6 that lies in the first…

A:

Q: x³ +1 Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = 1+²dy into the surface area of the object…

A: Find the arc length of y=x+2, 1≤x≤7 using the differential element ds=1+dxdy2dy. For formula for…

Q: 12. In the xy plane the region D is bounded by the lines y = 2x + 6 y = 2r +1, y = -3r +6, and y =…

A: Given: y=2x+6 y=2x+1 y=-3x+6 y=-3x+1

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: |(x+2y)d4, where D is the region bounded by the parabolas y=2x² D and y =1+x.

A:

Q: (1– y°)dx+(x° +e )dy, where C is the boundary of the region between the circles x2 + y2 = 4 and x2 +…

A: Given integral, ∮C1-y3dx+x3+ey2dy Here C is the boundary of the region between the circles x2+y2=4…

Q: 8. (x – y) dV, where E is enclosed by the surfaces z = x² – 1, z = 1 – x² , y = 0, and y = 2 E

A:

Q: Find the highest and lowest point (x, y, z) along the surface 8x +10y+ 4xy – x² – 2yʻ within the…

A: Given query is to find the highest and lowest point on the curve for the given region.

Q: Evaluate ||(x+2y)dA ,where D is the region bounded by the parabolas y = 2x² D and y=1+x².

A:

Q: Evaluate ffS. Vx² + y² dV, where E is the region tha lies inside the cylinder x? + y² = 16 and…

A:

Q: FIRd the absoluté ëxtrema of the function ƒ(x,y)= 3x² +2y -8y on the closed region bounded by y=x…

A:

Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 4 − x2, y = 0,…

A: Calculations: Point of intersection are given by: 4-x2 = 0 =>x2 = 4 =>x = -2, +2 Since, x…

Q: Q3. A- Use Greens theorem to evaluate the cireulation or flus for the velocity fiekd : S(x, y)=- *+y…

A: Given velocity field is  f(x,y)=1x+yi-1x+yj we have to find the flux for the boundary of square…

Q: Q2 (a) Find the volume under the surface z = 3x3 + 3x²y and over the rectangle R = {(x,y):1 < x <…

A:

Q: The region in the first quadrant is bounded by the curve y = 2 - x^2 and y = x^2. How far is the…

A: Given- The region in the first quadrant is bounded by the curve y = 2 - x2 and y = x2.  To find- How…

Q: Q3// 1. Sketch the region D and Evaluate: [ f(x+y) dA Where D, is the triangle region region in the…

A: Let's solve given double integration.

Q: 1. Find the region in the xy-plane in which the following equation is hyperbolic: [(x-y) -1]u +2uy…

A:

Q: When P = 0 Q2 Shade the area of the region bounded by the parabola, x² + p? – 2(p + 7)x – 5y + 59 +…

A:

Q: 2e+y dydx Evaluate t³ dydæ R where R is the semicircular region bounded by the x- axis and the curve…

A: I solve this by two methods but no options is correct

Q: The area of the region bounded by the curves r=y²+1 and y = x-3 is %3D 5. -1 -2 16 17 (A) 3 (B) 3…

A:

Q: Calculates the JR f(x,y)dA bounded by the given region I Loyan dA where the region S is given by the…

A:

Q: Evaluate ety - dx + ( 2xy + dy where C is a positively oriented boundary of the region enclosed by…

A:

Q: find the absolute maximum and minimum values of ƒ on the region R. ƒ(x, y) = x2 - y2 - 2x + 4y + 1…

A:

Q: Evaluate xydxdy over the region bounded by x axis, ordinate x = 2 and the curve y² = 4y %3D OA3 O B.…

A: To find: The value of ∫xydxdy over the region bounded by x- axis, ordinate x=2 and the curve x2=4y.…

Q: (b) ( y cos(ry) dA over the region R = {(x, y)|0<x < 1 and 1 < y <7/3}

A:

Q: 2ху dx + (x + у) dy Jc C: boundary of the region lying between the graphs of y = 0 and y = 1 – x2

A: Given: ∫C2xy dx+(x+y)dy y=0 and y=1-x2

Q: F = (2x- 5e" + sin(z'), –4ry + In(r'), 5z - 3r°y) %3D across the boundary of the region W = {(r, y,…

A: Given F=2x2-5ey+sinz2,-4xy+lnx4,5z-3x2y6

Q: $ (ry + sin(r + y²)) dx + (3x²y+2y sin(x + y²)) dy, where C is the clockwise boundary of the region…

A:

Q: b. $ (xy2 + sin(x + y?)) dx + (3x²y + 2y sin(x + y2))dy where C is the clockwise boundary of the…

A:

Q: By a suitable change of variables, evaluate ſf, dx dy where D is the region in the first quadrant…

A:

Q: Evaluate: ∬▒ 〖4X d A〗 over the region R bounded by the parabola Y = X ^ 2 and the line X = Y-2. A)9…

A:

Q: The absolute minimum of ƒ (x, y) = x² + y² – 4y on the semicircle region D = {(x, y) | y≥ 0, x² + y²…

A:

Q: Evaluate |(2y+cos x)dx + (5x+ sin y)dy along the positively oriented curve C. C is the boundary of…

A: We have to evaluate the integral ∫2y+cosxdx+5x+sinydy along the positively oriented curve C. Where C…

Q: Evaluate I/ V x2 + y2 dv, where E is the region that lies inside the cylinder x? + y2 = 9 and…

A:

Q: T Find the area of the plane region. 0≤x≤ bdunded by y=sin x. x = 2 2 1.111 s.u. π²-4 S.U. 1 s.u. EN…

A: We can solve this using given information

Q: Зу + 7eV X + 7ev x) dx + (10x + 7 cos(y?) ) dy C is the boundary of the region enclosed by the…

A:

Q: x² and t %3D 2) = z where E is the region bounded by the parabolic cylinder y

A: We have to set up the integral according to the given information

Q: $(2xy - x²) dx + (x+y²)dy, where C is the enclosed curve of the region boundec. The value of by y=x²…

A:

Q: =+ x²y) ds part of the cylinder y² + z² = 9 that lies between the planes x = 0 and x = 3 in the…

A: See the details solution in below

Q: Evaluate ſ. (3x² + y)dx + 4y²dy, where C is the boundary of the region in the first quadrant by y =…

A:

Q: on below Find c> 0 such that the area of the region enclosed by the parabolas y = x² – c² and y = c…

A:

Q: The value of $ (2xy - x²)dx+ (x+y²)dy, where C is the enclosed curve of the region bounded by y=x²…

A: As we know from the Green's theorem: ∫CMdx+Ndy=∫∫R∂N∂x-∂M∂ydA   I=∮2xy-x2dx+x+y2dy And C: y=x2, y2=x…

Q: The value of $(2xy - x²) dx + (x + y²)dy, where C is the enclosed curve of the region bounded by…

A:

Q: R where R is the semicircular region bounded by the x- axis and the curve y = v1 – x²

A: Double integral is used to integrate the function of two variable over a curve in two dimension. It…

Q: F(x, y) = (3x2 + y i + 3xy²j C: boundary of the region lying between the graphs of y = Vx, y = 0,…

A:

Q: f (x,y)= y² -2x² +10. Ris the region bounded by the parabola y = x and the line y = 4.

A: According to the given information, it is required to find the maximum and minimum value of f on the…

Q: [(x² - 2xy)dx + (x²y+3)dy ans: Verify Green's Theorem in plane for c of the region defined by y² =…

A: It is given that∫C(x2-2xy)dx+(x2y+3)dy. The objective is to verify Green's Theorem in plane for…

Q: Evaluate ||/ Væ² +y? dV, where E is the region that lies inside the cylinder æ² + y² = 16 and…

A: Given :  The integral ∫ ∫ ∫E x2+y2 dV , where E is the region that lies inside the cylinder  x2+y2 =…