The area bounded by y = 3, X = 2, y = -3 s and x = 0 is revolved about the y-axis 10. The x-coordinate of its centroid is. А. О В. 1 С. 2 D. 3

Q: Determine the equation of the normal line to the surface In (x + y) = Z 2 at the point (-1,2,0)

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Q: if x~unif. (0,2),find the U.b. of p(lx - mul>= 2)

A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: If z = In(x² – 2y), and x=u+v, y= e" , find and du If w=2xy'z', and y =x² +1, z= Vx, find dx

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Q: Find div F and curl F if F(x, y, z) = x³i - 10j+yzk. div F= curl F=

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Q: y" - y = coshx 10.

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Q: Draw the slope field and the trajectories (`integral curves") for the following equations. Show your…

A: Assume that y'=1c an arbitrary constant. So, from the given differential equation x=c. Thus, on…

Q: Find div F and curl F if F(x, y, z)=xi - 10j+yzk. div F= curl F=

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Q: 9- If a person with O'Micron virus coughs, It will spread the virus in a spherical form, determine…

A: Sol

Q: Can i get help step by step please?

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Q: The area of the sector of a curve having a radius of 250.00 feet and delta of 58° 32'12" is: a.…

A: Given query is to find the are of sector.

Q: y = v2x + (1//2) х2 +1

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Q: To/t Integrate Ua ko To 3. Uz kg 2. eT-1

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Q: Find the dimensions of a cylindrical can with a volume of 560 in^3 that minimizes the surface area.…

A: Let the radius of the cylindrical can be:  r Let the height of the cylindrical can be:  h

Q: Find the area of the portion of the unit sphere inside the cylinder x2 + y? = 1/2 and z > 0. Select…

A: The equation of the sphere is x2+y2+z2=r2. Here, r is the radius of the sphere. The equation of the…

Q: Find the area under the curve y = x^2 on [3, 10]. a. Use four rectangles. b. Find the exact area.

A: a)-We have   fx= x2We want to calculate over the interval 3, 10 with 4 rectangles, thus…

Q: What are the differential length, surfaces and volume for Cartesian coordinate system.

A: The question is taken from the Vector Calculus, and we have to give the answer the explanation for…

Q: Integrate by change of variable, ∫∫R(x + y)e((x^2)-(y^2))dA, where R is the rectangle enclosed by…

A: We need to evaluate integral.

Q: Express he equation n" = 4y in poar corinaes.

A: Given equation x2=4y

Q: Ass: 一 V EXAMPLE 6 Find the area enclosed by the line y = x - 1 and the parabola y² = 2x + 6.

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Q: Find equations of the tangent plane and normal line to the surface x=6y^2+5z^2−459 at the point (2,…

A: Find equations of the tangent plane and normal line to the surface x=6y^2+5z^2−459 at the point (2,…

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.