Find the area of one side of the “wall” standing orthogonally on the curve 2x + 3y = 6, 0<=x<= 6, and beneath the curve on the surface ƒ(x, y) = 4 + 3x + 2y

Q: Find the between the two curves. area 2. X=ay, a'y=x 3

A: The area between the curves can be calculated by integration. The formula used for the integration…

Q: Find the area of the surface formed by revolving the graph of f (x) = x2 on the interval [0,√2]…

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Q: The solid bounded by the surfaces S1: 2x + 3z = 6, S2: y = 2, S3: (y-2)² = 2x -2, S4: x = 0, S5: y =…

A: To find- The Solid bounded by the surfaces S1 : 2x + 3z = 6, S2 : y = 2, S3 : y - 22 = 2x - 2, S4 :…

Q: Find the area of the surface 2x^(3/2) + 2y^(3/2) - 3z = 0 above the square R: 0&lt;= x&lt;= 1,…

A: find z.

Q: The area of the surface obtained by rotating the curve y = 1sxse about the line x = 42 is

A: Given that y= 1/x  + x3 /12 and find the surface area. Here i attached solution of this question.

Q: Find the average squared distance between the origin and the points on the paraboloid z = 4 – x² –…

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Q: * = Vy +5,

A: We have to evaluate the area of the surface generated by revolving the curve  x=y+5 between the…

Q: Find the ar ea of sur face x - 2y - 2z = 0 that lies above the triangle bounded by the lines x = 2,…

A: Given :          The surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x…

Q: Find the moment of inertia of the region between the parabola y=4-x^2 and the line y=1-2x from x=0…

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Q: Find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

A: To find the surface area cut from the cone 2x2 + 2y2 = 5z2, z &gt; 0, by the cylinder x2 + y2 = 2y

Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: Find the center of mass and the moment of inertia about the y-axis of a thin plate bounded by the…

A:

Q: The area of the surface obtained by rotating the curve y = V9-x2, -1sxs1 about the x-axis is mit…

A: Use formula of surface area about x axis

Q: 9) Find a point on the surface z = 8- 3x2 - 2y2 at which the tangent plane is perpendicular to the…

A: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: Find the moment of inertia of the region between the parabola y = 6 − x2 and the line y = 1 – 2x…

A: Given, y=6-x2 and y=1-2x from x=0 to x=2

Q: Find the area of surface x2 – 2y – 2z = 0 that  lies above the triangle bounded by the lines x = 2,…

A:

Q: Find the area of the surface generated by revolving the curve y = √(x2 + 2), 0 ≤x ≤ √2, about the…

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Q: find the center of mass of a thin triangular plate bounded by y-axis and the line y = x and y = 2-x…

A: The triangular plate is bounded by y-axis, y=x,y=2-x if ∂x,y=6x+3y+3. Thus, the region is…

Q: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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Q: Find the area of the upper portion of the cylinder x2 + z2 = 1 that lies between the planes x = ±1/2…

A: Find the area of the upper portion of the cylinder x2 + z2 = 1 thatlies between the planes x = ±1/2…

Q: 17. Find the area of one side of the "winding wall" standing orthogonally on the curve x = y°, 0 < y…

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Q: Find the point (x, y, z) on the surface z = 2x2 - y where the tangent plane is parallel to the plane…

A: We have to find the point (x, y, z) on the surface z = 2x^2 - y^2 where the tangent plane is…

Q: Find the area of the surface generated by revolving the curve y=−x^3/18​, −2√2≤x≤0​, about the​…

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Q: Find the slope of the surface z = f (x, y) in the y-direction at the point (64, 8).

A: Follow the procedure given below.

Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Find the tangent plane of the function f(x, y) = √2x² + 2y² at (1,1). Is it parallel to 2- the plane…

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Q: Find the area of the surface x2 - 2y - 2z = 0 that lies above the triangle bounded by the lines x =…

A:

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A: Given problem is :

Q: 9) Find a point on the surface z = 8 – 3x2 – 2y² at which the tangent plane is perpendicular to the…

A: Given, Surface, z=8-3x2-2y2 at which the tangent plane is perpendicular to the line…

Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

A:

Q: ) Find the points on the ellipsoid 6x² + y² + 3z² = 4 where the tangent plane is parallel to the…

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Q: Find the points on the surface 1x^2+2y^2+5z^2=1 at which the tangent plane is parallel to the plane…

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

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Q: Find the equation of the tangent plane to the surface 3D1 16 at the point (1,-3,2) O a. 2x+4y-3z=12…

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Q: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 &lt;=x…

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Q: Find an equation of the tangent plane to the surface x-xyz 56 at the point (-4,5,2). Select one:…

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Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

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Q: Find the area of the surface of revolution generated by revolving C = {(x,y):x = y = 1- 2t, -1sts1}…

A: Given that C=x,y:x=-3+4t3, y=1-2t, -1≤t≤1 about the line x=2. The range of y is,…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0 ≤ x ≤ 1…

A: The formula for the surface area of the rotating object from the curve y=f(x) with the constraint…

Q: Find the surface area of the rotating object from the curve y = x^2 with the constraint 0< x <1…

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Q: Find the area of the surface that is generated by revolving the curve y= V16 – x² on the interval…

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Q: Find the area of the portion of the surface x2 - 2z = 0 that lies above the triangle bounded by the…

A: Definition used:

Q: x = 1+ 2y2, 1< x < 2 about the x-axis.

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: Find the surface area obtained by rotating y = V9 – x2 ,-2sxs-1 9– x² -2sxs-1

A: Given,             y=9-x2 , -2≤x≤-1

Q: Find the Surface area of the portión of the cylinder ya + z² =9 above the rectangle in the xy plane.…

A: Cylinder y2 + z2  = 9,z = 9-y2,0 ≤ x ≤ 2,and-3 ≤ y ≤ 3

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.