and above the region D in the ry-plane given by D = {(x, y) E R² | 0 < y < 1, y < z< Vy}.

Q: x² sin xy 14.5.8. || - dA(x, y), if D is the region bounded by æ² = "4, x² = TY, y² = ;, and D y? =…

A:

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

A:

Q: 4. Evaluate S, cos dA where D is the region bounded by D = {(x, y)/ VL < x < v3Ln , 0 < y< x² }.

A:

Q: D Evaluate xy dady where D is Hie region bounded x=0, y=0, and x+y= ! by

A:

Q: x dx + xy dy C.

A:

Q: Use Green's Theorem to evaluate the line integral. |v² dx + xy dy C: boundary of the region lying…

A: Introduction: The line integral ∫CF·dr geometrically represents the circulation of the function F…

Q: Use Green's Theorem to evaluate the line integral. y2 dx + xy dy C: boundary of the region lying…

A: Given: ∫Cy2 dx+xy dy, where C: boundary of the region lying between the graphs of y=0, y=x, and x=25…

Q: (b) y T= x (p) 3. Region bounded by: y = 4 – x² and y = 0. Rotate about: (a) the x-axis (с) у — —1

A: I have solved the first part for next parts repost the question

Q: c) Calculate (x+y + 2) dV, where E is the region bounded by r2 + y +z s 25 and above the E xy-plane.

A:

Q: y2 %3D 1. 60. x²y dx dy dz, T: Region bounded by 4

A:

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

A:

Q: 5xy dv, where E lies under the plane z = 1 + x + y and above the region in the xy-plane bounded by…

A: The given integral is ∭E5xydV. The region E lies under the plane z=1+x+y and above the region in the…

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: 11. xyz dV, where G is the solid in the first octant that is bounded by the parabolic cylinder z = 2…

A: To evaluate the triple integral

Q: Evaluate e dV where E is the region within the cylinder x? + y² = 2 bounded above by the paraboloid…

A:

Q: Use Green's Theorem to evaluate the line integral. | y2 dx + xy dy C: boundary of the region lying…

A:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A:

Q: Verify Green's Theorem by evaluating both integrals ƏN y2 dx + x² dy dA ay for the given path. C:…

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: 4. If C is the boundary of a region bounded by x2 + y? = 16 in counterclockwise manner, use Green's…

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: Evaluate the triple integral. 3xy dV, where E lies under the plane z = 1 + x + y and above the…

A:

Q: Evaluate (x+ y) dx +xy dy, where Cis the positively-oriented boundary of the region bounded by the…

A:

Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: Use Green's Theorem to evaluate the line integral. y2 dx + ху dy C: boundary of the region lying…

A: Use green s theorem

Q: Evaluate the triple integral. 2xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Final answer is 65/84.

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: ]]] xyz dV if S is the region bounded above by x² + y² +2²= 16 and below the S cone 2 = √² + y² with…

A:

Q: Use Green's Theorem to evaluate the line integral. √y² dx + xy dy C: boundary of the region lying…

A: We have to evaluate the integral.

Q: Use Green's Theorem to evaluate the line integral. | 2xy dx + (x + y) dy C: boundary of the region…

A:

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

A:

Q: Evaluate the triple integral. SSSE 7xy dV¸ where E lies under the plane = 1+x+ y and above the…

A: We have to Evaluate the triple integral.

Q: Let A be the region bounded by y = 8x 3(1−x) and the x-axis between x= 0 and x= 1. Find the solid…

A:

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

A:

Q: Evaluate the triple integral. 7xy dV, where E lies under the plane z = 1 + x + y and above the…

A:

Q: ∫c ( e^(y^2) +x)dy + (y^2 +arctan (sqrtx))dx where C is the region bounded by y = -x, y=-1 and x=2

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 evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: Line integration by using Greens theorem

Q: SSR (r + y)2 dA, where R is the region bounded by the limaçon r = 2 + cos 0

A:

Q: Use Green's theorem to evaluate the integral: 6(-x²y)dx + xy°dy where C is the boundary of the…

A: Let C be a positively oriented, piecewise smooth, simple, closed curve and let D be the region…

Q: Evaluate the triple integral. 4xy dV, where E lies under the plane z = 1 + x + y and above the…

A:

Q: Use Green's Theorem to evaluate the line integral. S y² dx + xy dy C: boundary of the region lying…

A:

Q: Use Green's Theorem to evaluate the line integral. 2xy dx + (x + y) dy C: boundary of the region…

A: First I have changed the line integral into double integral with the help of Green's theorem and…

Q: Evaluate (x+ y)dx+ xy dy. where Cis the positively-oriented boundary of the region bounded by the…

A: We have to evaluate the integral                                                  ∮Cx+ydx+xydy Where…

Q: Evaluate the triple integral. 5xy dV, where E lies under the plane z = 1 + x + y and above the…

A: Given that z=1+x+y The range of the variables are, 0≤x≤10≤≤x0≤z≤1+x+y Then, the integral is,…

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

A:

Q: A. Evaluate and sketch the line integral :1 = f yx dx + (2X – Y)dy around the region bounded by…

A: Greens theorem

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

A:

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.