2. Find the absolute maximum and minimum of f on the given region R: f(x, y) = 4 + 2x² + y², R = {(x, y) : –1 < I< 1,-1

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = •[ f(x) dx + [90 g(x) dx,…

A: First we identify the region by plotting (sketching) it.

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: 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: The region bounded by x = 1 - y¹, x = 0 is rotate about the line y = -5. The volume of the resulting…

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Q: F(x, y, z) = (x3, 0, z3), S is the boundary of the region in the first octant of space given by x2 +…

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Q: Evaluate (2r+y) dV _ where V is closed region bounded by the z= 4>x and the planes x = 0, y = 0 and…

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Q: Let R be the region bounded by y = 5 sin(x , y = 5(x – 2)²,

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Q: Suppose that f (x, y) satisfies f(-x,y) = –f(x, y). Give an /| s(x, y) dA = 0. example of a region D…

A: As per our guidelines we are supposed to answer only One question if there are multiple questions…

Q: Let f(x, y) = æ² + y + xy + 4 %3| and R be the region r2 + y? <1 Find the absolute maximum value of…

A: The objective is to find the absolute maximum value of the function.

Q: Integrate f(x, y, z) = x over the region in the first octant (x 2 0, y 2 0, z 2 0) above z = y2 and…

A: Given that,

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: A lamina is in the shape of the region bounded by the lines x = 1 and y = 2, and the parabola y =…

A: Let's find.

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: Find the absolute maximum and minimum values of f(x, y) = x² +y²+x²y+4 on the region = {(x, y) : |x|…

A: Consider the domain Ω=(x, y): |x|≤1, |y|≤1 We first find critical points by setting fx and fy equal…

Q: 11. Find the absolute extrema values of f(x, y) = y² – 6x² – 2y over the region on the xy-plane…

A: The values of absolute maximum or absolute minimum can be calculate by first obtaining the critical…

Q: The area of the region bounded by the z-axis and the curve = ²t - 1, y = 1-t² equals to: [2(1-1²)e²…

A: Solution

Q: y + x -0,x-1 and y=0,y-1-xto T.of u- dydx in terms of (u)and (v) given that: Region bounded R: x…

A: Evaluate, ∬Ry+x-4x-2y2-412dydx                        …1 Region R: x=0, x=1 and y=0, y=1-x u=2y+2x2…

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

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Q: The base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The…

A: Given, The base of a solid is the region bounded by the graphs of y = 3x,y = 6, and x = 0. The…

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 +…

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

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Q: 5.5 Find the volume of the solid bounded above by the graph of f(x, y) = xy sin(x²y) and below by…

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Q: Let R be the region bounded by the parabola y = x 2 − 1 and the line y = x+ 1 and let f(x, y) = xy…

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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: 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: 2 2 5. Find the volume of the solid bounded by the surface f (x, y) = 3x´y´ and the curves y = 2x -…

A: We will have to find the volume of the solid bounded by the surface f(x,y)=3x2y2 and the curves…

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

A:

Q: Find the areas of the regions 1. Bounded by the spiral r = 0 for 0 < 0 < T r = 0 2'2 х (п, т)

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

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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:…

A:

Q: Consider the region bounded above by the function z = 1/(x+3)2(y+7)2 and below by the xy plane for x…

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Q: Find the (absolute) maximum and minimum values of f(x, y) = 2x^2 + y^2 on the region R given by the…

A: We have to find the (absolute) maximum and minimum values of fx,y=2x2+y2 on the region R given by…

Q: Find the centroid of the region bounded by the graphs of the inequalities

A: Given information: y≤14x2          ...(1)x-42+y2≤16              ...(2)y≥0                ...(3)

Q: Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are x =…

A:

Q: Let R be the region bounded by the parabola y = x 2 − 1 and the line y = x+ 1 and let f(x, y) = xy…

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Q: 2. Find the centroid of the region bounded by the parabola y=x² and the line y=4.

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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: It is possible for a region in the xy-plane to be both type 1 and type 2 at the same time.

A: This is possible.

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: 3.) Find the area of the surface given by f (x, y) = 9 – x2 over the region R: square with vertices…

A: Given: fx,y=9-x2

Q: R is the region bounded by the lines y = x, y = -x, and x = 1. %3D

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Q: Sketch the region enclosed by the given curves. x = 9y2, x = 4 + 5y2 У y 1.0- 0.5 6. -0.5 o-1.0-…

A: Given curves are

Q: 2. Find the surface area of the solid generated by rotating the region bounded by the graphs of f(x)…

A: In this question we have to find the surface are of the solid region generated by rotating the…

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.…

A: We will find this using formula. As per our guidelines we are supposed to answer only one question.…