(d) |// Vx² + y² dV, where P is the region under the cone z = 2 – ry-plane. /x² + y² and above the (e) (4x – 2z) dV, where K is the region bounded by z = y², x = 0, x = 4, and z = 1.

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: Determine a region of the xy-plane for which the DE (y- x) y' = y+ xwill have a unique solution…

A: Consider a differential equation y'=F(x,y), y(x0)=y0. Then there exist a unique solution to this…

Q: The area of the region bounded by the curves 2y2 +2 and z 2y+2 is 2. 3 5 -1 -2 16 17 (A) 3 (B) 3 13…

A:

Q: Evaluate JJ, xy dA, where D is the region bounded by the curves xy = 2,4y = x² and y = 4. а.

A:

Q: A region R is bounded by the graphs of  y=0.8 (x)^1/2 and y=0.8x.  Find the moments Mx and My of R…

A: Given,

Q: Rotate the region bounded by x = y² – 6y + 10 and x = 5 about the y-axis

A: Solution :-

Q: 2. Evaluate f (3x + 4y2) dA, where R is the region in the upper half-plane 15 bounded by the circles…

A:

Q: Verify: Green's theorem in the plane for f(2x-y³) dx-xydy, where C is the boundary of the region…

A: Given information ∫c2x-y3dx-xydy Here, C is the boundary of the region enclosed by the circle…

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: Determine a region of the xy-plane for which the DE (1+ y) y' = x²will have a unique solution whose…

A: Theorem of existence of uniqueness: If f(x,y) and dfdy are continuous on rectangular region R, then…

Q: Rotate the region bounded by y = 6e 2" and y = 6+ 4x - 2x between a = 0 and a = 1 about the line y =…

A:

Q: Verify Green's theorem in the plane for f (32 - Sy*)dz + (4y – 6zy)dy, where C is the boundary of…

A:

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

A: We can help you with the question. I am not sure how to help you with its attachments.

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

A:

Q: 9. Evaluate 18x dV where E' is the region behind the surface y = 4 - 2² that is in front of the…

A:

Q: Evaluate the triple integral (x + 2y) dV where E is bounded by the parabolic cylinder y = 7x² and…

A:

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: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the cone z = Vr2 + y²…

A: In cylindrical coordinates,                                                               and…

Q: The numerical value of f3dA 3dA (where D is the region bounded by lines y=0 and x= 1 and the…

A:

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…

A:

Q: 8. Use Green's Theorem to calculate f, x?y³dx + (xy - y?)dy where C is the boundary of the region…

A: The given integral is ∫Cx2y3dx+xy-y2dy, where C is the boundary of the region lying between the…

Q: (b) ||| ryz dV if S is the region bounded above by x² + y² + z² = 16 and below the %3D Vr2 + y? with…

A:

Q: Where is the centroid of the region bounded by y = x2, y = 0, and x = 1?

A: First we find the area of the region bounded by the curve area A=∫01f(x) dx=∫01x2…

Q: 3. Evaluate /// 2* dV if G is a solid in the first octant bounded by the plane y + z = 2 and the…

A: triple integral

Q: Evaluate the moment M, and My of the region bounded by x- 2y - y? and the y-axis.

A: Given area is bounded by x=2y-y2 and y-axis.  On the y-axis, x=0. We try to find the point of…

Q: Q7. Use Green's theorem to evaluate fy² dx + 3xy dy, where c is the boundary of the semi annular…

A:

Q: Evaluate || Vx2 +y? dx dy over the region R in the xy plane bounded by x² +y² = 36 - R

A:

Q: Use Green's Theorem to calculate S,x²y³dx + (xy – y²)dy where C is the boundary of the region lying…

A: Greens Theorem:

Q: Use Green's Theorem to evaluate nds, where F = (Va+ 6y, 3x + 6y) C is the boundary of the region…

A: Given that        F = < √x + 6y , 3x + 6y > C is the boundary of the region enclosed by y=x-x2…

Q: Evaluate x dV , where E is the E region in the first octant bounded by the sphere x² + y² + z² = 1…

A: given region is in the first octant. using spherical coordinates x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ and…

Q: Let D be the solid region bounded above by z = -5x² +y? and below by z =-5. Then the projection of D…

A:

Q: Q7. Use Green's theorem to evaluate y² dx + 3xy dy, where c is the boundary o the semi annular…

A:

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

A:

Q: 2. Let R be the region in the first quadrant of the xy-plane bounded by the hyperbolas xy = 1, xy =…

A:

Q: Verify Green's theorem in the plane for S(3x² -8y )dx +(4y-6xy)dy, Where C is the boundary of the…

A:

Q: E is the region behind the surface y = 4 – x² that is in front of the region in the xy-plane bounded…

A: Given integral: ∫∬E18x dV Given that E is the region behind the surface y=4-x2 that is in front of…

Q: 3. Find the centroid of the region bounded by y 3-e, y0, 0, and 2. Since 0, z = 0, and x-2. Since…

A: The given region is bound by three straight line i.e. y = 0, x = 0 and x = 2 and one curve y =…

Q: Evaluate the triple integral -p (x + 6y) dV where E is bounded by the parabolic cylinder y = 8x² and…

A:

Q: Evaluate z dV where E is the region bounded between the spheres x² + y² + z² = 1 and x² + y? + z° 4…

A:

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,…

A:

Q: Compute s F=

A:

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: Evaluate the triple integral (x + 8y) dV where E is bounded by the parabolic cylinder y = 4x² and…

A:

Q: Q1 Verify that [(v ²– 2x )dx +(2xy +x³\dy = | dA where C is the boundary of a region %3D дх ду R…

A: By  apply green theorem

Q: 1. Find So(r+2y)dA, where D is the region bounded by the parabolas y r, and y=1+

A:

Q: Verify Green's theorem in the plane for (3x² -8y²)dx+(4y-6xy)dy, where C is the closed curve of the…

A:

Q: Evaluate the integral ₁²+ y (x+y)e³-²dA, where R is the region bounded by the lines z+y = 1 and 2 +…

A:

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

A: