Use the change of variables X = u, y = uv to evaluate ex dA, where R is the region R in the xy-plane bounded by the lines x = 1, x = 3, y = x, and

Q: Convert the double integral to uv-plane where R is the rectangle enclosed by the lines z- y = 0, x –…

A: Here, We need to convert the given double integral to uv-plane.

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

A: From Green's theorem, ∫CMdx+Ndy=∬∂N∂x-∂M∂ydydx If M=y2 ;N=xy, then ∂N∂x=y ; ∂M∂y=2y

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

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Q: Consider the double integral //(y - x) dæ dy I = R where the finite region R is bounded by the lines…

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Q: Evaluate dA where R is the region given by 0sxs 1, 0s y s 1.

A: The question is taken from the calculus in which we have to find the double integral value  so We…

Q: Evaluate J, (2x + y) dV, where V is closed region bounded by the cylinder : = 4 – and the planes 4.…

A: Q. Evaluate ∭V(2x+y)dV, where V is closed region bounded by the cylinder z=4-x2 and the planes x=0,…

Q: Sketch the region enclosed by 2y = 5/ã, y = 4, and 2y + 2x = 7. Decide whether to integrate with…

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Q: Calculate f 4y dydx, Where R is a region bounded by y=x* and y= - 3x2 - 2 R

A: Solution has been attached as an image

Q: Evaluate fSr f (x, y) dx dy, where R is the region given by 0< x< 2; 0 < y 5 5 and f(x, y) = 1 – –…

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Q: Sketch the region enclosed by 2y=SQRT(5x), y=4, and 2y+3x=8. Decide whether to integrate with…

A: From the geometry..

Q: Find the area of region enclosed by x = t – t“, y =t – t°, 0 <t < 1 using Green's Theorem.

A: The solution are next step..

Q: Find the area of the plane region bounded by the given curves: y= x^3, y= x + 6, and 2y+2 = 0

A: Explanation of the answer is as follows

Q: Evaluate SSA, dA, where R is the region bounded by y=x2 and x = y² in the first quadrant. X

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Q: A solid figure is created by rotating the region R around the x-axis. R is bounded by the curve y =…

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Q: 4/ Math

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Q: express the intergral ∫∫2x dA, as iterated intergral, where R is the region bounded by y=x+12 and…

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Q: Sketch the region enclosed by 2y = 5/T, y = 3, and 2y +2x 7. Decide whether to integrate with…

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Q: Use the change of variables s = xy, t = xy² to compute Sr xy² dA, where R is the region bounded by…

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Q: Evaluate ||xy dA, where R is the finite region in the first quadrant bounded by the R curves y=x²…

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Q: (b) |(x+y)dA} where R is the region bounded by y=Jx and y = x² .

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Q: Use the region R with the indicated boundaries to evaluate double integral.

A: Use the Fubini's theorem, ∬f(x,y)dA=∫ab∫cdf(x,y)dydx and write the double integral, ∬x2y2dxdy as…

Q: Find the double integral ∬R(x+y)dxdy, where the region R is a parallelogram with the sides y=x,…

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Q: Sketch the region R and evaluate the iterated integral J Fox, v) da. 18 6. (x + y) dx dy

A:

Q: Use the region R with the indicated boundaries to evaluate double integral.

A: ∫R∫ 4-4x2 dydx, 0≤x≤1, 0≤y≤2-2x

Q: O Evaluate (9te"")dn + (ex+ Gary)dy where C is the boundary of the region enclared by 4x* and x=y?…

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Q: Sketch the region R and evaluate the iterated integral f(x, y) dA. 18 (x + y) dx dy

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Q: Sketch the region enclosed by 2y = 5/T, y = 3, and 2y+2x = 7. Decide whether to integrate with…

A:

Q: Evaluate the moment Mx and M, of the region bounded by y = 2x + 1, x + y = 7 and x = 8.

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Q: Evaluate F dV where F = 3i+z j+2yk and V V is region bounded by planes z = 0, z = 3 = 4. and surface…

A: here I am simply using the property that triple integral gives volume and double integration area of…

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

A: A detailed solution is given below

Q: Use the change of variables u = y and v= xy to evaluate xydA, over the region R bounded by y= x, y3…

A: As per the instruction, we will be using change of variables u = y/x and v = xy to evaluate the…

Q: ) Evaluate Sxy dx dy R is the region bounded by x =0, x =2, y = x

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Q: On the x,y – plane, R is the region bounded by y=-Vx, y=-2/x, x=1, and x=4. (a) Sketch the region R.…

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Q: Let T be the triangular region bounded by the lines x + y = 1, x = 0, and y = 0. Evaluate the line…

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Q: Find the area of region enclosed by x = t – t", y =t – t°, 0 < t < 1 using Green's Theorem.

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Q: Integrate f(x, y) = x over the region D bounded by y = x2 and y = 6x + 7 x dA 1152

A: According to the given information, it is required to integrate the function f(x,y) over region D.

Q: Sketch the region R and evaluate the iterated integral f(x, y) dA. 30 15 (x + y) dx dy 16 30 14

A: We have to sketch the region and evaluate the integral:

Q: Let R denote the region in the first quadrant of the ry-plane that is bounded by y = V4 – x², y =…

A: Explanation of the answer is as follows

Q: Use the change of variabless = xy, t = xy to compute /R xy dA, where R is the region bounded by xy =…

A: The given region is: R= xy=1,  xy=6,  xy2=1,  xy2=6

Q: Find the area of region enclosed by x = t – t, y = t – tº, 0 < t < 1 using Green's Theorem.

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Q: SR(xy)dA where R is the region bounded by x=0, y=2x+1 and y=-2x+9.

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Q: ) Use Green's Theorem to evaluate [(x' -x'y)dx+ xy°dy] where C is the boundary of the region bounded…

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Q: Use the change of variables x = u - v, y= 2uw to evaluate the integral ley dA, where Ris the region…

A: Given: x=u2-v2and y=2uv  We need to evaluate ∬RydA , where R is the angle region bounded by the…

Q: SS ez+ydydx where R is the region bounded by: r = 0, y = 0, x + y = 1. Calculate the value of

A: The given integral is ∫∫Rex-yx+ydxdy where R is the region given as x=0; y=0; x+y=1. Change the…

Q: Sketch the region enclosed by 2y=4 sqrt(x), y=3, and 2y+3x=7. Decide whether to integrate with…

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Q: Evaluate 6xy dA over the region R enclosed between the curves R y = Vx, 2y = x, x = 2 and x = 4. %3D

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Q: Evaluate the line integral [2y'dx+(x* +6y°x)dy where C is the boundary of the R region shown below…

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

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Q: Evaluate the integral z dr dy dz where V is the region bounded by the planes 2x+y+2 1 = 0, y= 0, z…

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Q: Calculate the double integral (ir + 4y + 24) dA where R is the region: 0 <x < 2, 0<y< 3.

A: we have to find the following double integral

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.