3. Determine the absolute maximum and minimum values of f(x,y) = 2+4x-2x²+4y-y² %3D on the region R bounded by the x-axis, the lines y = 3x and x = 2.

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

A:

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

A: Solution :-

Q: 2/ Find the area of the region enclosed by the curves y=lx) and 0on the interven-4] A3 B. D, IS

A: Given: Area enclosed by y=|x| and y=0 on the interval [-1,4]

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

A:

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: Let R be the region bounded by the curve y = x and the line y = 2x. Use inequal- ities to describe R…

A: To describe: The region R using inequalities in terms of its vertical cross-sections. Calculation:…

Q: Sketch the region D = {(x, y, z): x2 + y2 ≤ 4, 0 ≤ z ≤ 4}.

A:

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

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: R is the region bounded by the functions f(x) +2 and the g(x) 1 r and the lines x-0 and x-4.…

A: Given fx=x+2 and gx=1-xand the lines x=0, x=4

Q: 8. Find the absolute extrema of the function f(x,y)=2x-2xy + y² over the region R. R is the region…

A:

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: 4. Find the volume of the solid generated when the region bounded X - 2 by f(x) = x = 1, and the…

A:

Q: The triangular region Ω has vertices (1, 1), (2, 0), and (2, 3).

A: My=∫12∫-x+22x-1kx2dydx

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

A:

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: 15. Find the area of the region enclosed by the curve x = y³ – y' and the line x = 2y. (Hint: Need…

A: We are asked to find the area of the region

Q: 3. The region bounded by y = x³, y = x, x > 0 is rotated about the x – - axis.

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: Sketch the bounded region enclosed by y=e^4x,y=e^9x and x=1. Decide whether to integrate with…

A:

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

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

A:

Q: and the y-axis. 2. Evaluate , 5x³ cos(y³) dA, where D is the region bounded by y = 2, y =:

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Calculate the Pntegrals over the defined region . y=-2x and y=1-2x on paralleberaM clased with Rhes.…

A:

Q: Consider the following equations. 1 x² O 6 Sketch the region bounded by the graphs of the equations.…

A: Given: y=1x2, y=4, x=6. To be find: area enclosed by given curves. Concept: the areaA of region R…

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: integrate ƒ over the given region. ƒ(x, y) = x/y over the region in the first quadrant bounded by…

A: Given

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

A: Use greens theorem

Q: 5. Evaluate the double integral Sſpx² + xy dxdy where D is the regiom bounded by y = x², x – axis…

A: We have to evaluate the double integral ∫∫Dx2+xy dxdy  , where D is the region  We first sketch the…

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

A:

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

A:

Q: 2. The area bounded by y = -(x - 1)2 + 4, and the lines x =1, y = 2, and y = 4 rotated about the %3D…

A:

Q: Integrate f(x, y) = x over the region bounded by y = x 2 and y = X + 2.

A: This is the region. x2 = x + 2   x2 - x-2 = 0 x = 2 or x = -1 so , to integrating in the region.…

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: 1- Integrate The furction F(X,y= over The region bounded byrj=X7y=2x9 x =1/X=?

A: According to our company guideline if multiple questions are posted we must do only first. You can…

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

A:

Q: Q3. The region bounded by the curve y x² and the line y 3x, is revolved about the line x = -3. Find…

A: Here i use cylindrical shell method to find out volume of rotation

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

A:

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

A:

Q: Find the absolute maximum and minimum values of f(x, y) = 4 + 2x2+y2on the region R={(x,…

A:

Q: Let h(x, y) = 2x² – 2x²y + y². Find the absolute minimum and maximum values of the surface on the…

A: We use partial derivative to find critical points to check maximum and minimum value

Q: The region is bounded by y = x³, y = 2x + 4 and y = −1. Then Arearegion = [₁ f(x) dx + f[ g(x) dx,…

A:

Q: Find the absolute extrema of f(x,y) = 3x² + xy on the region bounded by the parabola y = x² and the…

A: differentiate the function partially with respect to x and y fx=6x+yfy=x Put the obtained function…