The formula of calculating the surface area with equation z = f (x, y), where and are Ôx ôy continuous is given as S = +1 dA . Ôy Ôx Find the surface area of the part of the food container z = Jx? + y² that lies inside the cylinder x² + y2 = 2x . Sketch the region R.

Q: Find the surface area in r(r,0)=(rcos)i + (rsin0) j+0k, 0≤0≤2ñ, 0≤r≤1. the accompanying (1, 0, 2)…

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the area in the first quadrant bounded by the curve y = 3x – x, the lines x = y = 2. 0 and

A: To find the area of the region bounded by the curve we use the formula Area=∫abf(x)-g(x)…

Q: Determine the area of the region enclosed by y=sinx and y=cosx, x=π/2 and the y- axis .

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Q: Sketch the curves y = 3x and y = x and determine the area enclosed by them.

A: we can find the area enclosed by the curve by setting up the double integral. to find the limit of…

Q: Find the area of the plane region bounded by the curves y = √x − 1, y = 3, the x-axis, and the…

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Q: Find the surface area of the solid obtained by rotating the graph of y = Vx, 1<y<2 around the…

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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.