under the cone Z =Vx²+y² and above the region bounded by the semicircle X=-V 4-y and the y-axis.

Q: Find the minimum distance from the point (2, -1, 1) to the plane x + y - z = 2.

A:

Q: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

A:

Q: Find the centroids of the function, y=4x-x^2, y=x (please sketch the graph)

A: Let's find.

Q: Q3: Find the points on the surface x^2+z^2-630, closest to the origin.

A:

Q: Find the centroid of the region cut from the first quadrant by the circle x2 + y2 = a2.

A:

Q: Q1) Find plane area bounded by y = 2,y = 6 – x, and y = 8 - 3x using double %3D

A:

Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: Sketch the surface 1≤z≤√√9-x²-y²_and_x² + y² ≤

A: Solution is below

Q: Find the area of the plane region that lies below the line y = 2x and between the parabolas y= 2x^2…

A: Given Curves are:…

Q: Sketch one loop of the curve 9y² = x(3x)² Find the area of the surface of revolution generated by…

A:

Q: to Rind the points Lagrange multiplier surface (x-1)(y-2)(Z-)=| near est Qz use on the to the point…

A:

Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

A:

Q: EX- Find the area of the surface generated by rotating the 1 portion of the curve y= (x²+2)³ between…

A:

Q: Find the area of the plane x−2y+5z=13 cut out by the cylinder x^2+y^2=9

A:

Q: Draw a contour map of g(x,y)=y^2−x^2.  Be sure to label the k value of each level curve.

A: given gx,y=y2-x2

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.